An oriented matroid is a mathematical structure that abstracts the properties of directed graphs, vector arrangements over ordered fields, and hyperplane...

connected flip graph. Each rank-3 oriented matroid is equivalent to an arrangement of pseudolines, and each oriented matroid which is also uniform (in which...

In combinatorics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many...

discussion, but it makes no material difference. Supersolvable arrangement Oriented matroid "Arrangement of hyperplanes", Encyclopedia of Mathematics, EMS Press...

Configurations Line arrangements Hyperplane arrangements Buildings An oriented matroid is a mathematical structure that abstracts the properties of directed...

based on his previous papers on oriented-matroid theory. However, Bland's rule exhibits cycling on some oriented-matroid linear-programming problems. The...

termed "Bland oriented matroids" by Jack Edmonds. Another pivoting rule, the criss-cross algorithm, avoids cycles on all oriented-matroid linear-programs...

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

cocircuits of M {\displaystyle {\mathcal {M}}} and if we consider the oriented matroid M {\displaystyle {\mathcal {M}}} represented by M {\displaystyle {M}}...

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

of a rank-3 oriented matroid. The points and lines of geometries defined using other number systems than the real numbers also form matroids, but not necessarily...

2010.01.018, MR 2601261. 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 matroids, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the...

another geometric lattice of the same rank. The Vámos matroid can be oriented. In oriented matroids, a form of the Hahn–Banach theorem follows from a certain...

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

semialgebraic set is equivalent to the space of realizations of an oriented matroid. 1994: Louis Billera for finding bases of piecewise-polynomial function...

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

programming Odds algorithm used to solve optimal stopping problems Oriented matroid Quadratic programming, a superset of linear programming Semidefinite...

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

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

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

Such LCPs can be solved when they are formulated abstractly using oriented-matroid theory. Complementarity theory Physics engine Impulse/constraint type...

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

for his contributions to optimization, polyhedral computation and oriented matroid theory. Fukuda is a professor in optimization and computational geometry...

(computer networking) Flow graph (disambiguation) Max-flow min-cut theorem Oriented matroid Shortest path problem Nowhere-zero flow A.V. Goldberg, É. Tardos and...

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

Versions of the Shannon switching game played on a directed graph and an oriented matroid have been described for theoretical purposes; but no corresponding...

In matroid theory, a Sylvester matroid is a matroid in which every pair of elements belongs to a three-element circuit (a triangle) of the matroid. In...

mathematics and computer science, a matroid oracle is a subroutine through which an algorithm may access a matroid, an abstract combinatorial structure...

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...