M(G)} is called a cycle matroid. Matroids derived in this way are graphic matroids. Not every matroid is graphic, but all matroids on three elements are...

edge lengths one or the square root of two are exactly the delta-matroids. Matroid polytopes are members of the family of generalized permutohedra. Let...

ordered. All oriented matroids have an underlying matroid. Thus, results on ordinary matroids can be applied to oriented matroids. However, the converse...

structure from which the matroid was defined for graphic matroids, transversal matroids, gammoids, and linear matroids, and for matroids formed from these by...

linear matroids. However, it is NP-hard for certain compactly-represented matroids, and requires more than a polynomial number of steps in the matroid oracle...

Matroid, Inc. is a computer vision company that offers a platform for creating computer vision models, called detectors, to search visual media for objects...

delta-matroids. Delta-matroids have also been used to study constraint satisfaction problems. As a special case, an even delta-matroid is a delta-matroid in...

and algebraic matroids coincide, but for other fields there may exist algebraic matroids that are not linear; indeed the non-Pappus matroid is algebraic...

finite undirected graph. The dual matroids of graphic matroids are called co-graphic matroids or bond matroids. A matroid that is both graphic and co-graphic...

almost all matroids are paving matroids. Every simple matroid of rank three is a paving matroid; for instance this is true of the Fano matroid. The Vámos...

circuits. For matroids that are not binary, the duality between Eulerian and bipartite matroids may break down. For instance, the uniform matroid U 6 4 {\displaystyle...

In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which...

Matroid partitioning is a problem arising in the mathematical study of matroids and in the design and analysis of algorithms. Its goal is to partition...

binary matroids (which include the graphic matroids derived from planar graphs): a binary matroid is Eulerian if and only if its dual matroid is bipartite...

be independent sets of a matroid. The input to this problem is a set S of items, a positive integer m, and some m matroids over the same set S. The goal...

{\displaystyle x} in A {\displaystyle A} . A basic problem regarding weighted matroids is to find an independent set with a maximum total weight. This problem...

gammoids are exactly the dual matroids of the transversal matroids. To see that every strict gammoid is dual to a transversal matroid, let γ {\displaystyle \gamma...

In combinatorics, a matroid embedding is a set system (F, E), where F is a collection of feasible sets, that satisfies the following properties. Accessibility...

the matroid intersection problem is to find a largest common independent set in two matroids over the same ground set. If the elements of the matroid are...

Systems for a Matroid", pp. 7–9. Federico, Ardila (2012). "Matroids: Lecture 6". Youtube. White, Neil, ed. (1986), Theory of Matroids, Encyclopedia of...

same element of B. There are matroids that are base-orderable but not strongly-base-orderable. In base-orderable matroids, a feasible exchange bijection...

transversal matroids in general, bicircular matroids form a minor-closed class; that is, any submatroid or contraction of a bicircular matroid is also a...

bases of the rigidity matroid of the complete graph) is an important open problem. Graver, Jack E. (1991), "Rigidity matroids", SIAM Journal on Discrete...

of matroids, a minor of a matroid M is another matroid N that is obtained from M by a sequence of restriction and contraction operations. Matroid minors...

theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations...

smaller matroids. The direct sum of a family of uniform matroids (not necessarily all with the same parameters) is called a partition matroid. Every uniform...

equals the rank function of the matroid. The Vámos matroid is not a secret-sharing matroid. Secret-sharing matroids describe "ideal" secret sharing schemes...

binary matroids. However, there exist non-binary matroids for which this duality breaks down. Any algorithm that tests whether a given matroid is binary...

set disjoint from it. Matroid duals go back to the original paper by Hassler Whitney defining matroids. They generalize to matroids the notions of plane...

} In matroid theory, two particularly important special classes of matroids are the wheel matroids and the whirl matroids, both derived from...

mathematics, Coxeter matroids are generalization of matroids depending on a choice of a Coxeter group W and a parabolic subgroup P. Ordinary matroids correspond...

regular matroids: every non-regular matroid has at least one of these three as a minor. Thus, the regular matroids are exactly the matroids that do not...

problems on matroids where the objective function of the optimization depends on the set of colors chosen as part of a matroid basis. Bipartite matroid Rota's...

compute, but fixed-parameter tractable for linear matroids when parameterized both by the matroid rank and the field size of a linear representation...

theory of matroids, Santa Monica, Calif.: RAND Corporation report R-446-PR. Also Tutte, W. T. (1971), Introduction to the theory of matroids, Modern analytic...

structure theory of matroids. Excluding the Fano plane as a matroid minor is necessary to characterize several important classes of matroids, such as regular...

matroids are representable over no fields at all. The matroids that are representable over a particular field form a proper subclass of all matroids....

theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements of the matroid is, similarly...

uniform matroid U n n {\displaystyle U{}_{n}^{n}} . The unique basis of this matroid is the ground-set itself, E. Among matroids on E, the free matroid on...

has been proven for paving matroids (for all n) and for the case n ≤ 3 (for all types of matroid). For arbitrary matroids, it is possible to arrange the...

Institute of Technology. His doctoral dissertation was titled, On Infinite Matroids, PhD in 1970 from Cornell University. Wagstaff was one of the founding...

In a Sylvester matroid, every independent set can be augmented by one more element to form a circuit of the matroid. Sylvester matroids (other than U n...

oriented matroids. In this context, the result of Kelly & Moser (1958) lower-bounding the number of ordinary lines can be generalized to oriented matroids: every...

(2010–2016) The Bergman complex of a matroid and phylogenetic trees (2003), with Carly Klivans Lagrangian geometry of matroids (2020), with Graham Denham and...

graph; when applied to characterising sparsity, matroids describe certain sets of sparse graphs. These matroids are connected to the structural rigidity of...

section 2.5, "Bon-matroid of a graph", pp. 5–6, section 5.6, "Graphic and co-graphic matroids", pp. 19–20, and section 9, "Graphic matroids", pp. 38–47....

to Cornell in 1978. Bland is known as one of the inventors of oriented matroids, which he used to define Bland's rule for avoiding cycles in the simplex...

matroids is known, but certain matroids are known to be non-algebraic; the smallest is the Vámos matroid. Many finite matroids may be represented by a matrix...

In the mathematics of matroids and lattices, a geometric lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic semimodular...

B is unbalanced. Biased graphs are interesting mostly because of their matroids, but also because of their connection with multiary quasigroups. See below...

{\displaystyle n-r} . In the case of linear matroids this coincides with the matrix corank. In the case of graphic matroids the corank is also known as the circuit...

Gian-Carlo Rota in the context of matroid theory: there are dozens of equivalent axiomatic approaches to matroids, but two different systems of axioms...

binary matroids, matroids representable over GF(2): a binary matroid is Eulerian if and only if it is the contraction of another binary matroid onto a...

of the matroids representable over the three-element field; and a theorem that all regular matroids consist of graphic and cographic matroids, and a special...

this has been proven only for the matroids of bounded branchwidth. Additionally, if a minor-closed family of matroids representable over a finite field...

dominant of the spanning set polytope of matroids. Footnotes Edmonds, Jack. Submodular functions, matroids, and certain polyhedra. 1970. Combinatorial...

n-dimensional Euclidean space Flat (matroids), a further generalization of flats from linear algebra to the context of matroids Flat module in ring theory Flat...

3-sums of graphic matroids (the matroids representing spanning trees in a graph), cographic matroids, and a certain 10-element matroid. Lovász (2006). As...

Thus the combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic...

cannot be oriented; it is one of several known minor-minimal non-orientable matroids. The solution to Möbius' problem of mutually inscribed polygons for values...

hypercube. Zonotopes are intimately connected to hyperplane arrangements and matroid theory. The Minkowski sum of a finite set of line segments in R d {\displaystyle...

271, pp. 485–499. Thomas Zaslavsky (1991), Biased graphs. II. The three matroids. Journal of Combinatorial Theory, Series B, Vol. 51, pp. 46–72. Thomas...

springs Tutte homotopy theorem, on the composition of generalized paths in matroids Hanani–Tutte theorem on the parity of edge crossings in graph drawings...

extension complexity. On the other hand, the independence polytope of regular matroids has polynomial extension complexity. The notion of extension complexity...

Coxeter matroids; it was published by Serganova and Israel Gelfand in 1987 as part of their research originating the concept of a Coxeter matroid. "Book...

be extended from graphs to matroids. An ear decomposition of a matroid is defined to be a sequence of circuits of the matroid, with two properties: each...

Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Karim Adiprasito, he is one of the five winners of the 2019 New Horizons...

Björner et alia, Chapters 1-3. Bokowski, Chapters 1-4. Because matroids and oriented matroids are abstractions of other mathematical abstractions, nearly...

are two matroids associated with a signed graph, called the signed-graphic matroid (also called the frame matroid or sometimes bias matroid) and the...

on algebraic combinatorics, analytic combinatorics, graph theory, and matroid theory. Until December 2019, the journal was edited by George Andrews,...

S. R. Murty (1971) Equicardinal matroids. Journal of Combinatorial Theory, Series B U. S. R. Murty (1970) Matroids with Sylvester property. Aequationes...

applications in information theory, matroid theory, and network coding. There are interesting connections between matroids, the entropy region and group theory...

Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Joseph Rabinoff and David Zureick-Brown, he has given bounds on rational...

geometry. His work on matroids culminated in the paper "Representation of matroids" published in 1969. In his work, Ingleton studied matroids as a generalization...

theorem. Arrangement of lines Oriented matroid Coxeter group Dr. Lukas Finschi, "Homepage of Oriented Matroids" Handbook of Discrete and Computational...

model theory, infinite finitary matroids, there called "pregeometries" (and "geometries" if they are simple matroids), are used in the discussion of independence...

the abstract setting of oriented matroids, Bland's rule cycles on some examples. A restricted class of oriented matroids on which Bland's rule avoids cycling...

Chapel Hill. Her dissertation, Affine Hyperplane Arrangements and Oriented Matroids, was supervised by Thomas H. Brylawski. She joined the University of Montana...

was a Japanese mathematician who independently invented the theory of matroids, though his work was forgotten for many years. He published four papers...

algebras, Boolean algebras, distributive lattices, and geometric lattices (matroids). These lattice-like structures all admit order-theoretic as well as algebraic...

(sets of size 2), and their vertices (sets of size 1). In the context of matroids and greedoids, abstract simplicial complexes are also called independence...

Specht module may be found in Section 1 of "Specht Polytopes and Specht Matroids". The dimension of the Specht module V λ {\displaystyle V_{\lambda }} is...

Proudfoot, Nicholas; Young, Benjamin (2017). "Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures" (PDF). Séminaire Lotharingien de...

Thus the combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic...

Intersection of two partition matroids - 6.75 Intersection of a graphic matroid and a partition matroid - 10.66 General matroid with matroid rank k {\displaystyle...

the graph. Analogously, we may define matroids from pseudoforests. For any graph G = (V,E), we may define a matroid on the edges of G, in which a set of...

polynomial does not generalize to matroids because k(A) is not a matroid property: different graphs with the same matroid can have different numbers of connected...

The rank of a subset X of E is the size of a basis of X. Just as with matroids, greedoids have a cryptomorphism in terms of rank functions. A function...

sets of a matroid. For example, every bundle must contain at most k items, where k is a fixed integer (this corresponds to a uniform matroid). Or, the...

introduced by Tutte (1958), generalises the concept of "path" from graphs to matroids, and states roughly that closed paths can be written as compositions of...

machine learning. He is adjunct professor at Stanford University, CEO of Matroid, and a founding team member at Databricks. His work focuses on machine...

monograph with Springer, Boolean Representations of Simplicial Complexes and Matroids. John Rhodes and Benjamin Steinberg (2008), The q-theory of finite semigroups...

G may be described using matroid theory as the dual rank of the graphic matroid of G. Using the greedy property of matroids, this means that one can find...

Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Huh, he is one of five winners of the 2019 New Horizons Prize for...

its original position horizontally, vertically, or diagonally, and 185 matroids on five labeled elements in which each element participates in at least...

object. In a matroid, every subset of an independent set is again independent. This is a hereditary property of sets. A family of matroids may have a hereditary...

used to determine the number of bases in regular matroids, a generalization of the graphic matroids (Maurer 1976). Kirchhoff's theorem can be modified...

his research themes had as their main subject graphs, hypergraphs and matroids, and were linked to famous and difficult problems in Graph coloring and...

fractions Greedy source Hill climbing Horizon effect Matroid Feige, Uriel. "Greedy algorithms and Matroids" (PDF). Department of Computer Science and Applied...

specializing in graph theory, including the interplay among graph minors, matroid theory, tree decomposition, and infinite graphs. He holds the chair of...

optimization. He is known for his work on matroid theory and the extension of the Graph Minors Project to representable matroids. In 2003, he won the Fulkerson Prize...

graph theory culminated in a 1933 paper where he laid the foundations for matroids, a fundamental notion in modern combinatorics and representation theory...

an important graph invariant, and is closely related to invariants of matroids, topological spaces, and matrices. In random graphs, a frequently occurring...

In mathematical optimization, Cunningham's rule (also known as least recently considered rule or round-robin rule) is an algorithmic refinement of the...

area of matroids. He found a polyhedral description for all spanning trees of a graph, and more generally for all independent sets of a matroid. Building...

nodes, 68 different degree sequences of four-node connected graphs, and 68 matroids on four labeled elements. Størmer's theorem proves that, for every number...

Mathematical Association of America for his expository article An introduction to matroid theory. Due to his collaboration on a 1977 paper with the Hungarian mathematician...

configurations) appear in a characterization of the graphic matroids by forbidden matroid minors. Wagner, K. (1937), "Über eine Eigenschaft der ebenen...

Coding theory, including error correcting codes and a part of cryptography Matroid theory Discrete geometry Discrete probability distributions Game theory...

mathematical underpinnings related to the Brouwer fixed-point theorem, matroids and graph connectivity. Hex is a finite, two-player perfect information...

Michel Las Vergnas, and Jim Lawrence.. Workshop program, Combinatorial geometries: matroids, oriented matroids and applications, retrieved 2013-11-03....

(ビービネイル, Bībi Neiru) to enlarge the Matroids. Metal Alice is voiced by Marina Inoue (井上 麻里奈, Inoue Marina). The Matroids (マトロイド, Matoroido) are the Matrintis...

University. Her dissertation, Minors of 3-Connected Matroids and Adjoints of Binary Matroids, concerned matroid theory and was supervised by Robert E. Bixby...

Mathematics at Louisiana State University. He is known for his expertise in matroid theory and graph theory. Oxley did his undergraduate studies in Australia...

analogous to peripheral cycles, but not the same even in graphic matroids (the matroids whose circuits are the simple cycles of a graph). For example, in...

semimodular bounded lattice is called a matroid lattice because such lattices are equivalent to (simple) matroids. An atomistic semimodular bounded lattice...

algebraic (or semialgebraic) varieties as realization spaces of oriented matroids. Informally it can also be understood as the statement that point configurations...

geometric lattices and matroids, this lattice of partitions of a finite set corresponds to a matroid in which the base set of the matroid consists of the atoms...

use it to describe separation in graphs. This usage has been extended to matroids. The balance of this article discusses Conway's sense of tangles; for the...

oriented matroids. The criss-cross algorithm has been adapted for problems that are more complicated than linear programming: There are oriented-matroid variants...

E(M)}(x-1)^{r(E)-r(A)}(y-1)^{|A|-r(A)}} is the generalization of the Tutte polynomial to matroids. The invariant is named after Alexander Grothendieck because of a similar...

MR 2991468. Lawler, E.L. (1976), Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston Eiselt, H. A.; Gendreau, Michel; Laporte, Gilbert...

pointy appearance in certain drawings) and their graphic matroids have been called thagomizer matroids. Triangular books form one of the key building blocks...

unified in matroid theory by the girth of a matroid, the size of the smallest dependent set in the matroid. For a graphic matroid, the matroid girth equals...

for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof...

vector. Matroid rank functions Let Ω = { e 1 , e 2 , … , e n } {\displaystyle \Omega =\{e_{1},e_{2},\dots ,e_{n}\}} be the ground set on which a matroid is...

unified in matroid theory by the girth of a matroid, the size of the smallest dependent set in the matroid. For a graphic matroid, the matroid girth equals...

optimization are: combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures integer programming constraint programming...

length of a shortest cycle contained in a graph Matroid girth, the size of the smallest circuit in a matroid Girth (album), 1997 album by heavy metal band...

matroids. In this context, the core of a convex cost game is called the base polyhedron, because its elements generalize base properties of matroids....

MR 2155721, S2CID 14391276. Whiteley, Walter (1988), "The union of matroids and the rigidity of frameworks", SIAM Journal on Discrete Mathematics,...

transformation to a more general computational problem on matroids, the matroid parity problem for linear matroids. Beineke, Lowell W.; Wilson, Robin J. (2009), Topics...

algebraic geometry; her research has also involved algebraic combinatorics, matroid theory, Hermitian matrices, and spectrahedra in convex optimization. She...

Vol. 47, 32–52. Thomas Zaslavsky (1991), Biased graphs. II. The three matroids. Journal of Combinatorial Theory, Series B, Vol. 51, 46–72. Thomas Zaslavsky...

1961. Elsevier. ISBN 9781483223568. Kazuo Murota (2009). Matrices and Matroids for Systems Analysis. Springer Science & Business Media. p. 47. ISBN 9783642039942...

factor-criticality has been extended to matroids by defining a type of ear decomposition on matroids and defining a matroid to be factor-critical if it has an...

oriented matroids; in particular, the Folkman–Lawrence topological representation theorem is "one of the cornerstones of the theory of oriented matroids". In...

semilattice, there is an analogous matroid-like structure called a semimatroid, which is a generalization of a matroid (and has the same relationship to...

professor of Oxford University's Mathematical Institute. He was an expert in matroid theory, the computational complexity of combinatorial enumeration problems...

set of vectors in a vector space. Independent set of elements of a matroid. See Matroid#Independent sets. Independent set (graph theory), a set of vertices...

Lawler, Eugene L. (1976), "Chapter 9: The Matroid Parity Problem", Combinatorial Optimization: Networks and Matroids, New York: Holt, Rinehart and Winston...

of bipartiteness to hypergraphs. Bipartite matroid, a class of matroids that includes the graphic matroids of bipartite graphs Bipartite network projection...

also be expressed using the theory of matroids, according to which a spanning tree is a base of the graphic matroid, a fundamental cycle is the unique circuit...

Bokowski, J.; Guedes de Oliveira, A. (2000), "On the generation of oriented matroids", Discrete and Computational Geometry, 24 (2–3): 197–208, doi:10.1007/s004540010027...

bound than that for the k {\displaystyle k} -set problem. For more general matroids, Dey's O ( n k 1 / 3 ) {\displaystyle O(nk^{1/3})} upper bound has a matching...

Yahya Ould; Las Vergnas, Michel (1986). "Directed switching on graphs and matroids". Journal of Combinatorial Theory. Series B. 40 (3): 237–239. doi:10...

rigid graphs, and they form the bases of the two-dimensional rigidity matroids. If n points in the plane are given, then there are 2n degrees of freedom...

research student of Peter Vámos. His doctoral thesis was "Representations of Matroids". Fenton was a postdoctoral fellow in the mathematics department at University...

recognizing the generalization by Saunders Mac Lane of Steinitz's lemma to matroids. Let U {\displaystyle U} and W {\displaystyle W} be finite subsets of a...

Missouri. Her research interests include combinatorics, graph theory, and matroids. Carolyn Mahoney was born the sixth of thirteen children in 1946 in Memphis...

Brigitte Irma Servatius (born 1954) is a mathematician specializing in matroids and structural rigidity. She is a professor of mathematics at Worcester...

Method of computing optimal strategies for last-success problems Oriented matroid – Abstraction of ordered linear algebra Quadratic programming – Solving...

(2007). "On D.K. Biss' papers "The homotopy type of the matroid Grassmannian" and "Oriented matroids, complex manifolds, and a combinatorial model for BU""...

(graph theory), a symmetric tessellation of a closed surface Regular matroid, a matroid which can be represented over any field Regular paperfolding sequence...

reduction can in fact be performed as the complex is constructed by using matroid theory, leading to further performance increases. Another recent algorithm...

the University of North Carolina, Chapel Hill. He worked primarily in matroid theory. Brylawski was born in 1944, and grew up in Washington, D.C. He...

has led to a deeper understanding of distributions on spanning trees and matroid bases in general and to a revolution in the understanding of Markov Chain...

(graph theory), a relation of one graph to another Minor (matroid theory), a relation of one matroid to another Minor (linear algebra), the determinant of...

to determine the existence of a transversal which is independent in a matroid. Hall 1986, pg. 51. An alternative form of the marriage theorem applies...

White, Neil; Ziegler, Günter (1999). "10 Linear programming". Oriented Matroids. Cambridge University Press. pp. 417–479. doi:10.1017/CBO9780511586507...

|V|=\max(|F|,\dim V).} A vector space can be seen as a particular case of a matroid, and in the latter there is a well-defined notion of dimension. The length...

other repeated vertices than the starting and ending vertices Circuit of a matroid Circuit (neural network), a computational subgraph within an artificial...

and that this definition does agree with matrix rank as here discussed. Matroid rank Nonnegative rank (linear algebra) Rank (differential topology) Rank–nullity...

of Mathematical Logic, University of Leeds Aubrey William Ingleton 1967 Matroids Fellow Robin Wilson 1962 graph theory Professor, Open University public...

an infinite matroid, or pregeometry. A model of a strongly minimal theory is determined up to isomorphism by its dimension as a matroid. Totally categorical...

S and X to the case where X has a matroid structure and matchings must match to an independent set in the matroid on X. The Klarner–Rado Sequence is...

elements, or a matroid constraint where the elements have a known matroid structure and we want to only accept an independent set of the matroid. Prophet inequalities...

pregeometry has several meanings: Pregeometry (model theory), another name for a matroid Pregeometry (physics), a structure from which geometry arises This disambiguation...

defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom, antimatroids are defined instead...

ISSN 0022-0000. Eugene Lawler (2001). "4. Network Flows". Combinatorial Optimization: Networks and Matroids. Dover. pp. 109–177. ISBN 978-0-486-41453-9....

(2009). A Lost Mathematician, Takeo Nakasawa: The Forgotten Father of Matroid Theory. Springer. p. 15. Hosie, Alexander (1910). Manchuria; its people...

the graphic matroid of a graph, a subset of edges is independent if the corresponding subgraph is a tree or forest. In the bicircular matroid, a subset...

set for the group Rank of a Lie group – see Cartan subgroup Rank of a matroid, the maximal size of an independent set Rank of a partition, at least two...

polyhedra, it is by now also capable of dealing with simplicial complexes, matroids, polyhedral fans, graphs, tropical objects, toric varieties and other objects...

seminal. The rational singularity and fundamental cycles, which are used in matroid theory, are such examples of his sheer originality and thinking. He began...

2-coloring and 3-coloring for graphs, in the matroid intersection problem for intersections of two or three matroids, and in 2-SAT and 3-SAT for satisfiability...

hdl:1721.1/138650. Crapo, Henry H. (1965), "Single-element extensions of matroids", Journal of Research of the National Bureau of Standards Section B, 69B...

mathematical structures other than graphs, and in particular in vector spaces and matroids. Two algorithmic problems are associated with MISs: finding a single MIS...

(1983, p. 79) There are abstract optimization problems, called oriented matroid programs, on which Bland's rule cycles (incorrectly) while the criss-cross...

1007/978-3-319-44914-2_9. In P: Seymour, P. D. (June 1980). "Decomposition of regular matroids" (PDF). Journal of Combinatorial Theory, Series B. 28 (3): 305–359. doi:10...

matroid theory, the family of sets complementary to the independent sets of a given matroid themselves form another matroid, called the dual matroid....

special case of a more general matroid partitioning problem, in which one wishes to express a set of elements of a matroid as a union of a small number...

Title Role Episodes Tensou Sentai Goseiger Matroid Metal Alice of the Agent 33-44 Kaizoku Sentai Gokaiger Metal Alice of the Agent 40...

Dougherty, Randall; Freiling, Chris; Zeger, Kenneth (2007), "Networks, matroids, and non-Shannon information inequalities", IEEE Transactions on Information...

"Isotropic matroids I: Multimatroids and neighborhoods". arXiv:1503.04406 [math.CO]. Brijder, Robert; Traldi, Lorenzo (2016-10-19). "Isotropic matroids II: Circle...

random oracle). Black box group Turing reduction Interactive proof system Matroid oracle Demand oracle Padding oracle attack van Melkebeek 2003, Section...

education, and is known for his expertise in structural rigidity and rigidity matroids. Whiteley graduated from Queen's University in 1966. He earned his Ph.D...

bridgeless and almost-Eulerian), but they do not contain each other. Eulerian matroid, an abstract generalization of Eulerian graphs Five room puzzle Handshaking...

they allow for higher-dimensional simplices. Every graph gives rise to a matroid. In model theory, a graph is just a structure. But in that case, there...

Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter (1999), Oriented matroids, Encyclopedia of Mathematics and Its Applications, vol. 46 (2nd ed.), Cambridge...

Archived from the original on 2012-11-02. Retrieved 2009-04-26. Review of Matroids, motives, and a conjecture of Kontsevich MR 1950482 "Home page". Patrick...

(2009). A Lost Mathematician, Takeo Nakasawa: The Forgotten Father of Matroid Theory. Springer. p. 15. Philippe Forêt (January 2000). Mapping Chengde:...

S2CID 27202372. Lawler, E. L. Combinatorial Optimization: Networks and Matroids. 1976. Mirsky, Leon (1971). Transversal Theory: An account of some aspects...

Grötschel, Martin (2004), "Cardinality homogeneous set systems, cycles in matroids, and associated polytopes", The Sharpest Cut: The Impact of Manfred Padberg...

linear complementarity and their combinatorial abstractions in oriented matroids. With Tamás Terlaky, Fukuda worked on a particular class of pivot algorithms...

theorem. Paul Seymour for generalizing the max-flow min-cut theorem to matroids. 1982: D.B. Judin, Arkadi Nemirovski, Leonid Khachiyan, Martin Grötschel...

G} form the bases of a matroid. Cameron, P. J; Fon-Der-Flaass, D. G (1995-11-01). "Bases for permutation groups and matroids". European Journal of Combinatorics...

MR 2000133 Borovik, Alexandre V.; Gelfand, I. M.; White, Neil (2003), Coxeter matroids, Progress in Mathematics, vol. 216, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3764-4...

configuration. This matroid and its dual matroid have been applied in characterizing certain classes of matroids that are linear matroids over the finite...

Berkeley Max Planck Institute for Mathematics in the Sciences Thesis Oriented Matroids and Combinatorial Convex Geometry; Computational Synthetic Geometry Doctoral...

1090/s0002-9939-1969-0236029-9. MR 0236029. Brualdi, Richard A. (1971). "Induced matroids". Proc. Amer. Math. Soc. 29 (2): 213–221. doi:10.1090/s0002-9939-1971-0289335-5...

deprecated parameter |citeseerx= (help). Murty, U. S. R. (1969), "Sylvester matroids", Recent Progress in Combinatorics (Proc. Third Waterloo Conf. on Combinatorics...

Lawler, Eugene L. (2001), Combinatorial Optimization: Networks and Matroids, Courier Dover Publications, p. 64, ISBN 978-0-486-41453-9. Sedgewick,...

(1972), Cheng and Liu (2007), and Gutman and Borovićanin (2011). In the matroid theory the nullity of the graph is the nullity of the oriented incidence...

minimums of finite collections of polynomials. Rota's basis conjecture: for matroids of rank n {\displaystyle n} with n {\displaystyle n} disjoint bases B i...

cube, the Browder–Minty theorem, the introduction of oriented regular matroids, and the Minty-Vitaver theorem on graph coloring. George Minty Jr. grew...

doctoral dissertation, The Transversal Presentations and Graphs of Bicircular Matroids, was supervised by Richard A. Brualdi. Neudauer has been funded by the...

finds applications in error-correction codes, compressive sensing, and matroid theory, and provides a simple criterion for maximal sparsity of solutions...

1112/blms/18.6.571, MR 0859948 Ramírez Alfonsín, J. L. (2001), "Lawrence oriented matroids and a problem of McMullen on projective equivalences of polytopes", European...

of Max-Flow Min-Cut Theorem". Combinatorial Optimization: Networks and Matroids. Dover. pp. 117–120. ISBN 0-486-41453-1. Lemaréchal, Claude (2001). "Lagrangian...

In mathematical optimization, Zadeh's rule (also known as the least-entered rule) is an algorithmic refinement of the simplex method for linear optimization...

graph Nullity, the difference between the size and rank of a subset in a matroid Nullity, a concept in wheel theory denoted by ⊥, or similarly in transreal...

truncations, and duals of matroids. Chapter three concerns graphic matroids, the matroids of spanning trees in graphs, and the greedy algorithm for minimum...

node to itself Cycle graph, a graph that is itself a cycle Cycle matroid, a matroid derived from the cycle structure of a graph Cycle (sequence), a sequence...

2017-04-17 Lindström, Bernt (1973), On the vector representations of induced matroids, doi:10.1112/blms/5.1.85 Sagan, Bruce E. (2001), The symmetric group, Springer...

Combinatorial Theory, Series B, 96(3), 388–404. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original...

Schrijver, 1988, vol. 2; 2nd ed., 1993) Systems Analysis by Graphs and Matroids (Kazuo Murota, 1987, vol. 3) Greedoids (Bernhard Korte, László Lovász,...

190. Lawler, Eugene L. (2001), Combinatorial optimization: networks and matroids, Dover Publications, pp. 222–223, ISBN 978-0-486-41453-9. "Prove that the...

of a relation is the smallest equivalence relation that contains it. In matroid theory, the closure of X is the largest superset of X that has the same...

convex hulls may also be generalized in a more abstract way, to oriented matroids. It is not obvious that the first definition makes sense: why should there...

affine Gale diagrams can also be described through the duality of oriented matroids. As with the linear diagram, a subset of vertices forms a face if and only...

polynomial time, by transforming them into an instance of the matroid parity problem for linear matroids. Connected dominating sets are useful in the computation...

Bokowski, J.; Guedes de Oliveira, A. (2000), "On the Generation of Oriented Matroids", Discrete & Computational Geometry, 24: 197–208, doi:10.1007/s004540010027...

3247570. S2CID 248986512. Kühne, L.; Yashfe, G. (2022). "Representability of Matroids by c-Arrangements is Undecidable". Israel Journal of Mathematics. 252:...

of disjoint cycles. Cycle basis Cycle double cover conjecture Eulerian matroid Sabidussi 1964. Euler, L. (1736), "Solutio problematis ad geometriam situs...

applications of combinatorics. Series B is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and...

subset problem was studied with additional constraint represented by a matroid. Envy-free item allocation Participatory budgeting algorithm Multiwinner...

a bit-length which is not polynomial in this representation. Oriented matroid Nef polyhedron Steinitz's theorem for convex polyhedra Branko Grünbaum...

Frequency partition Graph partition Kernel of a function Lamination (topology) Matroid partitioning Multipartition Multiplicative partition Noncrossing partition...

(help) Lawler, Eugene (2001). Combinatorial Optimization: Networks and Matroids. Dover. ISBN 0-486-41453-1. Lee, Jon (2004). A First Course in Combinatorial...

and diversity. Topics in her research have included tropical geometry, matroid polytopes, Chow rings, toric varieties, lattices and semilattices, and...

Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating set of an ideal: Gröbner basis Hilbert's basis theorem Generating...

correspondence between CC systems and uniform acyclic oriented matroids of rank 3. These matroids in turn have a 1-1 correspondence to topological equivalence...

-graded sets. Signed sets are fundamental to the definition of oriented matroids. They may also be used to define the faces of a hypercube. If the hypercube...

Coloring can also be considered for signed graphs and gain graphs. Colored matroid Critical graph Graph coloring game Graph homomorphism Hajós construction...

abstract simplicial complex with the augmentation property is called a matroid. Laminar: for any two hyperedges, either they are disjoint, or one is included...

graph is the nullity of its adjacency matrix, which equals n − r. In the matroid theory of graphs the rank of an undirected graph is defined as the number...

the Witwatersrand, University of Cambridge, University of Waterloo Thesis Matroids on Complete Boolean Algebras  (1970) Doctoral advisor Gert Sabidussi...

Michael; Sturmfels, Bernd; White, Neil; Ziegler, Günter M. (1999). Oriented Matroids (2nd ed.). Cambridge University Press. ISBN 0-521-77750-X. Björner, Anders;...

terms: HYPERGRAPHS ⊃ INDEPENDENCE-SYSTEMS = ABSTRACT-SIMPLICIAL-COMPLEXES ⊃ MATROIDS. Bondy, Adrian; Murty, U.S.R. (2008), Graph Theory, Graduate Texts in Mathematics...

in field extensions both form examples of finitary matroids (pregeometries). Any finitary matroid has a basis, and all bases have the same cardinality...

which the concept of the dimension of a subspace is defined (see also Matroid § Hyperplanes (coatoms). The difference in dimension between a subspace...

June 2020). Carolina Benedetti, Quotients of positroids and lattice path matroids, AlCoVE 2020. Retrieved 16 July 2025 – via YouTube. Quiceno, Juan Diego...

 125–136. Ramirez Alfonsin, J. L. (1999), "Spatial graphs and oriented matroids: the trefoil", Discrete and Computational Geometry, 22 (1): 149–158, doi:10...

of it include enumerative combinatorics, combinatorial design theory, matroid theory, extremal combinatorics and algebraic combinatorics, as well as...

analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal...

example Dihedral angle (between two planes). See also Angles between flats.) Matroid Coplanarity Isometry Gallier, J. (2011). "Basics of Affine Geometry". Geometric...

His dissertation, Composition and Decomposition of Matroids and Related Topics, concerned matroid theory and was supervised by Louis Billera. His doctoral...

may refer to The characteristic set of an algebraic matroid The characteristic set of a linear matroid Wu's method of characteristic set This disambiguation...

For example, 1.2E3 is 1.2×103 or 1200 the set of edges in a graph or matroid the unit prefix exa (1018) energy in physics electric field denoted E {\displaystyle...

can be covered by edge-disjoint subgraphs. Arboricity Bridge (cut edge) Matroid partitioning Menger's theorem Tree packing conjecture Tutte, W. T. (1961)...

surfaces) Richard Rado's theorem (Ramsey theory) Richard Rado's theorem (matroid theory) This disambiguation page lists mathematics articles associated...

Marc Roth: Counting restricted homomorphisms via Möbius inversion over matroid lattice 2016 Stefan Kratsch: A randomized polynomial kernelization for...

e. is prime and minimal over) a strongly minimal set, which carries a matroid structure determined by (model-theoretic) algebraic closure that gives...

A. Harvey (MIT) "Algebraic Structures and Algorithms for Matching and Matroid Problems" 2005 Mark Braverman (Toronto) "On the Complexity of Real Functions"...

for constraint satisfaction problems, and width parameters in graphs and matroids. She is an associate professor at KAIST. Kim studied industrial engineering...

of choice is true. Thus the two assertions are equivalent. Basis of a matroid Basis of a linear program Coordinate system Change of basis – Coordinate...

Tutte) has "had a huge impact," in part because of its implications in matroid theory. Nash-Williams also studied k-edge-connected graphs, Hamiltonian...

York, 1994 Borovik, Alexandre V.; Gelfand, I. M.; White, Neil: Coxeter matroids. Progress in Mathematics, 216. Birkhäuser Boston, Inc., Boston, MA, 2003...

Lincoln University of Missouri Researched combinatorics, graph theory, and matroids Shirley M. Malcom zoologist 1946- Senior Advisor and Director of SEA Change...

planarity criterion that a graph is planar if and only if its graphic matroid is also cographic, Mac Lane's planarity criterion characterizing planar...

schemes defined by Kirchhoff polynomials to the representation spaces of matroids. Moreover, using Mnev's universality theorem, we show that these schemes...

ISBN 978-0-521-59840-8, MR 1477750. Las Vergnas, Michel (1980), "Convexity in oriented matroids", Journal of Combinatorial Theory, Series B, 29 (2): 231–243, doi:10...

independent and M 1 + ⋯ + M d = X . {\displaystyle M_{1}+\cdots +M_{d}=X.} Matroid – Abstraction of linear independence of vectors G. E. Shilov, Linear Algebra...

the bases of a matroid over the set of resources, then all best-response sequences converge in polynomial number of steps, and the matroid property is essential...

mathematics concerning the study of finite or countable discrete structures. Matroid Greedoid Ramsey theory Van der Waerden's theorem Hales–Jewett theorem Umbral...

also known as the Euler integral of the first kind Beta invariant, of a matroid Dirichlet beta function Eratosthenes, Greek mathematician nicknamed Beta...

Shinkenger: Kusare Ayakashi Azemidoro (ep. 31) Tensou Sentai Goseiger: Matroid Bakutofuji-ER of the Timer (ep. 39–40) Tokumei Sentai Go-Busters: Omochiloid...

M. (1992), "8. Introduction to greedoids" (PDF), in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics and its Applications, vol. 40...

1016/0024-3795(84)90147-2 Seymour, P. D. (1980), "Decomposition of regular matroids", Journal of Combinatorial Theory, Series B, 28 (3): 305–359, doi:10...

Munagala and Shah focus on three types of constraints: Matroid constraints: there is a fixed matroid M over the items, and the chosen items must form a basis...

Günter M. (1992), "Introduction to greedoids", in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics and its Applications, vol. 40...

independently published on the criss-cross algorithm. The theory of oriented matroids has also been used by Terlaky and Zhang (1991) to prove that their criss-cross...

Section 4.3 Aharoni, Ron; Berger, Eli (2006). "The intersection of a matroid and a simplicial complex". Transactions of the American Mathematical Society...

to the Grassmannian, neighbor joining in the space of metric trees, and matroids. Chapter five considers tropical analogues of some of the important concepts...

relation. This is equivalent to the definition of algebraic dependence. matroid This article incorporates material from Dependence relation on PlanetMath...

mathematics at Binghamton University since 1985. He has published papers on matroid theory, hyperplane arrangements, coding theory, lattice point counting...

concepts in structural (combinatorial) rigidity theory, such as the rigidity matroid. The following results concern the l p p {\displaystyle l_{p}^{p}} -distance...

of a set in F {\displaystyle F} is also in ⁠ F {\displaystyle F} ⁠. A matroid is an abstract simplicial complex with an additional property called the...

have smaller weight. By standard properties of bases in vector spaces and matroids, the minimum weight cycle basis not only minimizes the sum of the weights...

featured the antagonistic robot group Matrintis. Their foot soldiers, the Matroids, followed perverted versions of the "Three Laws of Robotics": conquer humans...

Federico Ardila, a Colombian mathematician specializing in combinatorics and matroid theory. In 2019, Khoe joined Ardila on a sabbatical which involved traveling...

helix Coxeter element Coxeter functor Coxeter graph Coxeter group Coxeter matroid Coxeter notation Coxeter's loxodromic sequence of tangent circles Coxeter–Dynkin...

first to recognize the importance of transversal matroids, and he showed that transversal matroids can be represented using linear algebra over transcendental...

the study of arrangements of pseudolines and (more generally) oriented matroids. His work with Pollack includes such results as the first nontrivial bounds...

In mathematics, a supersolvable arrangement is a hyperplane arrangement that has a maximal flag consisting of modular elements. Equivalently, the intersection...

non-crossing spanning trees of planar point sets, and more generally bases of matroids, using a state space that swaps one edge for another. Euler tours in graphs...

or a base of this matroid. Cardinality constraints are special cases of matroid constraints in which the matroid is a uniform matroid. Categorized cardinality...

definition of the span of points in space, a subset X of the ground set of a matroid is called a spanning set if the rank of X equals the rank of the entire...

networking) Flow graph (disambiguation) Max-flow min-cut theorem Oriented matroid Shortest path problem Nowhere-zero flow Active flow network A.V. Goldberg...

algorithms. 2018: Stefan Kratsch and Magnus Wahlström for their work using matroid theory to develop polynomial-size kernels for odd cycle transversal and...

Hall, Rhiannon; Oxley, James; Semple, Charles; Whittle, Geoff (2002). "On matroids of branch-width three". Journal of Combinatorial Theory, Series B. 86 (1):...

the Bron–Kerbosch algorithm Listing all elements of structures such as matroids and greedoids Several problems on graphs, e.g., enumerating independent...

Westermann, H. H. (1992), "Forests, frames, and games: algorithms for matroid sums and applications", Algorithmica, 7 (1): 465–497, doi:10.1007/BF01758774...

in any graph may be found in polynomial time using an algorithm for the matroid parity problem. Since triangular cactus graphs are planar graphs, the largest...

Sylvester–Gallai designs. A closely related concept is a Sylvester matroid, a matroid with the same property as a Sylvester–Gallai configuration of having...

 147, American Mathematical Society, pp. 125–136. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original...

3247570. S2CID 248986512. Kühne, L.; Yashfe, G. (2022). "Representability of Matroids by c-Arrangements is Undecidable". Israel Journal of Mathematics. 252:...

problems that includes as special cases the minimum-cost flow problem, matroid intersection, and the problem of computing a minimum-weight dijoin in a...

Sentai Shinkenger Ayakashi Yumebakura Ep. 25-26 2010 Tensou Sentai Goseiger Matroid Robogōgu of the 10-sai Eps. 33-43 2012 Tokumei Sentai Go-Busters Dumbbellloid...

in 2006. Her dissertation was supervised by T. James Reid and concerned matroid theory. She was the second African-American woman to earn a doctorate in...

. Filtration (mathematics) Flag (geometry) Flag manifold Grassmannian Matroid Kostrikin, Alexei I. and Manin, Yuri I. (1997). Linear Algebra and Geometry...

Mathematisch für fortgeschrittene Anfänger : Weitere beliebte Beiträge von Matroids Matheplanet (in German). Heidelberg: Spektrum Akademischer Verlag. pp. 273–276...

mathematical logician Brigitte Servatius (born 1954), Austrian-American expert on matroids and structural rigidity Nataša Šešum, expert in geometric flows Lena L...

Alexander; Krummeck, Vanessa; Richter-Gebert, Jurgen (2003). "Complex matroids: phirotopes and their realizations in rank 2". In Aronov, Boris; Basu,...

"The multivariate Tutte polynomial (Alias Potts model) for graphs and matroids". Surveys in Combinatorics 2005. pp. 173–226. arXiv:math/0503607. doi:10...

Thomas; Zhang, Yihao (2018-07-18). A tale of Santa Claus, hypergraphs and matroids. Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms...

Mathematical Society. ISBN 978-3-03719-017-3. Kazuo Murota (2009). Matrices and Matroids for Systems Analysis. Springer Science & Business Media. ISBN 978-3-642-03994-2...

S2CID 121878844 Golumbic, Martin Charles (1977), "Comparability graphs and a new matroid", Journal of Combinatorial Theory, Series B, 22 (1): 68–90, doi:10...

characteristic polynomial, making it a graph determined by its spectrum. Vámos matroid Weisstein, Eric W. "Diamond Graph". MathWorld. ISGCI: Information System...

(2014). "Polynomial-time T-count optimization of Clifford+T circuits via matroid partitioning". Proceedings of the 46th ACM Symposium on Theory of Computing...

Ardila, Federico; Klivans, Caroline J. (2006). "The Bergman complex of a matroid and phylogenetic trees". Journal of Combinatorial Theory, Series B. 96...

N. Gabow and R.E. Tarjan, Journal of the ACM 38, 4, 1991, 815-853. "A matroid approach to finding edge connectivity and packing arborescences," H.N....

(2003), Combinatorial optimization: Polyhedra and efficiency, Vol. B: Matroids, trees, stable sets, Algorithms and Combinatorics, vol. 24, Berlin: Springer-Verlag...

node for every clique of the underlying graph Partition matroid, a kind of matroid whose matroid intersections may form clique complexes Bandelt & Chepoi...

Robogorg struggles to understand how the Goseigers are destroying his Matroids, Metal Alice offers to personally oversee the next mission. Meanwhile,...

supersolvable, although it is not geometric. The lattice of flats of the graphic matroid for a graph is supersolvable if and only if the graph is chordal. Working...

operator (Cyclic decomposition of maximal monotone operator) Oriented matroids (realizable OMs and applications) Carathéodory's theorem (convex hull)...

of Max-Flow Min-Cut Theorem". Combinatorial Optimization: Networks and Matroids. Dover. pp. 117–120. ISBN 0-486-41453-1. Christos H. Papadimitriou, Kenneth...

Shinkenger (2009) (Ayakashi Sasamatage (ep. 20)) Tensou Sentai Goseiger (2010) (Matroid Adoborute-G of the Vital (ep. 37)) Albino Alligator (Milo (Gary Sinise))...

important contributions in diverse areas of discrete mathematics, including matroid theory, matching theory, the max-cut and stable set problems, spectral...

algebraic combinatorics, including work on cell complexes associated with matroids and on chip-firing games. She is an associate professor of applied mathematics...

D. thesis, University of California, Berkeley. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original...

"Cocircuit Graphs and Efficient Orientation Reconstruction in Oriented Matroids". Eur. J. Comb. 22 (5): 587–600. doi:10.1006/eujc.2001.0481. ISSN 0195-6698...

and using the Biswas-Barman algorithm for fair allocation with partition matroid constraints, or simply by round-robin item allocation. This guarantees...

finite obstruction set. Erdős–Hajnal conjecture Forbidden subgraph problem Matroid minor Zarankiewicz problem Diestel, Reinhard (2000), Graph Theory, Graduate...

"The multivariate Tutte polynomial (alias Potts model) for graphs and matroids". Surveys in Combinatorics 2005. pp. 173–226. arXiv:math/0503607. doi:10...

Monnot, Jérôme; Tlilane, Lydia (2015-07-19). "Worst case compromises in matroids with applications to the allocation of indivisible goods". Theoretical...

"type II" quasisymmetric power sums, and bases related to enumeration in matroids. Quasisymmetric functions have been applied in enumerative combinatorics...

A and {x}. A finitary closure operator with this property is called a matroid. The dimension of a vector space, or the transcendence degree of a field...

Günter M. (1992), "Introduction to Greedoids", in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics and its Applications, vol. 40...

polynomial time, by transforming it into an instance of the matroid parity problem for linear matroids. The special case of finding all feedback vertices in...

Westermann, Herbert H. (1992), "Forests, frames, and games: algorithms for matroid sums and applications", Algorithmica, 7 (5–6): 465–497, doi:10.1007/BF01758774...

Laurent; Monnot, Jérôme; Tlilane, Lydia (2014-08-18). "Near fairness in matroids". Proceedings of the Twenty-First European Conference on Artificial Intelligence...

several ways of constructing such graphs. Hobbs had also done research in matroid theory. Dr. Hobbs has 40 publications in graph theory, and in 1989 co-authored...

in any graph may be found in polynomial time using an algorithm for the matroid parity problem. Since triangular cactus graphs are planar graphs, the largest...

graph H. Graph minors are often studied in the more general context of matroid minors. In this context, it is common to assume that all graphs are connected...

Rider Decade (2009) – Garulu (ep. 4 - 5) Tensou Sentai Goseiger (2010) – Matroid Zuteru-S of the Mach (ep. 35) Kamen Rider × Kamen Rider Fourze & OOO: Movie...

Victoria University of Wellington The mathematics of space and language: matroids and model theory Robert McKay Victoria University of Wellington Antarctic...

equipped with a further oracle for determining element orders. Implicit graph Matroid oracle Babai, L.; Szemeredi, E. (1984). "On the Complexity of Matrix Group...

geometry has been founded, having close connection, for example, with matroid theory. Synthetic differential geometry is an application of topos theory...

public goods, with possible constraints on the allocation. They consider matroid constraints, matching constraints, and packing constraints (which correspond...

facets are available. Abstract polytope Combinatorial commutative algebra Matroid polytope Order polytope Simplicial sphere Stable matching polytope Ziegler...

The Avis–Fukuda algorithm adapted the criss-cross algorithm for oriented matroids. A 2025 article by Zelin Dong, Fenglei Fan, Huan Xiong, and Tieyong Zeng...

doi:10.1090/S0273-0979-1993-00335-5, MR 1164063. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original...

variant is known as the agreeable subset problem. There may be general matroid constraints, matching constraints or knapsack constraints on the chosen...

used by German armed forces during World War II, leading contributor to matroid and graph theory; as William Thomas Tutte, in Newmarket, Suffolk, England...

Goemans, Michel; Olver, Neil; Rothvoss, Thomas; Zenklusen, Rico (2012). "Matroids and integrality gaps for hypergraphic steiner tree relaxations". Proceedings...

applications. CRC Press. ISBN 0-8493-3982-0. Oxley, James (2006) [1992]. Matroid Theory. Oxford University Press. ISBN 978-0-19-920250-8. Rosen, Kenneth...

is t-dependent; the t-dependent families form the dependent sets of a matroid, which Deza and his co-authors investigate. Deza, M.; Laurent, M. (1992)...

framework of separoids; e.g., graphs, configurations of convex sets, oriented matroids, and polytopes. Any countable category is an induced subcategory of separoids...

Zan-KT0 of the Shot (ショットのザンKT0, Shotto no Zan Kē Tī Zero): A scallop-themed Matroid and servant of the Matrintis Empire. He is deployed to destroy the Negakure...

MR 1964792, S2CID 34821155. Las Vergnas, Michel (1980), "Convexity in oriented matroids", Journal of Combinatorial Theory, Series B, 29 (2): 231–243, doi:10...

In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector...

"Fractional Arboricity Strength and Principal Partitions in Graphs and Matroids". Discrete Applied Mathematics. 40 (3): 285–302. doi:10.1016/0166-218X(92)90002-R...

"Exponentially many hypohamiltonian graphs", Graphs, Hypergraphs and Matroids III (Proc. Conf. Kalsk 1988), Zielona Góra: Higher College of Engineering...

Thomas; Zhang, Yihao (2019-12-23), "A Tale of Santa Claus, Hypergraphs and Matroids", Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, Proceedings...

Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter M. (1993), Oriented Matroids, Encyclopedia of Mathematics and its Applications, vol. 46, Cambridge:...

incidence matrices, submodular set functions, independent matchings in matroids, the Birkhoff–von Neumann theorem on the Birkhoff polytope of doubly stochastic...

satisfying the second condition form the independent sets of a sparsity matroid, and are called ( 2 , 3 ) {\displaystyle (2,3)} -sparse. A graph satisfying...

(2012), no. 4, 911–922. 2013 Branch decomposition heuristics for linear matroids Archived October 15, 2018, at the Wayback Machine (with Jing Ma, Susan...

Stanley has had a big impact in contemporary combinatorics for his work in matroid theory, for introducing Zeta polynomials, for explicitly defining Eulerian...

Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter (1999), Oriented Matroids, Encyclopedia of Mathematics and Its Applications, vol. 46 (2nd ed.), Cambridge...

supply constraints given as an independence system over the items, such as matroid constraints. They focus on unit-demand buyers. Chen and Deng study multi-item...

Elad; Carmesin, Johannes; Fröhlich, Jan-Oliver (2012-07-09), Infinite matroid union, arXiv:1111.0602 Blossier, Thomas; Bouscaren, Elisabeth (2010). "Finitely...

fuzzy measures, fuzzy topological games, fuzzy commutative algebra, fuzzy matroids, etc. During the 79th Annual Conference of the Indian Mathematical Society...

(2007). "On D.K. Biss' papers 'The homotopy type of the matroid Grassmannian' and 'Oriented matroids, complex manifolds, and a combinatorial model for BU'"...

the LYM inequality) Lucas chain MacMahon's master theorem Magic square Matroid embedding Monge array Monomial order Moreau's necklace-counting function...

(2018). "Multiple exchange property for M♮-concave functions and valuated matroids". Mathematics of Operations Research. 43 (3): 781–788. arXiv:1608.07021...

the two configurations, including the fact that both are self-dual under Matroid duality. In abstract terms, the latter configuration has "points" 0, ....

group, an implicit model for group-theoretic algorithms Matroid oracle, an implicit model for matroid algorithms Korf, Richard E. (2008), "Linear-time disk-based...

Born: Takeo Nakasawa, Japanese mathematician, conceived the theory of matroid. His work was largely forgotten and would be rediscovered more than 60...

In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon)...

University in 1975, with the dissertation Comparability Graphs and a New Matroid supervised by Samuel Eilenberg. He became an assistant professor in the...

personal attendant, a Matrintis Empire marshal, and the first high-spec Matroid built by her master to serve him. Prior to her and Robogorg's battle with...