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

In combinatorics, a branch of mathematics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector...

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

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

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

varieties as realizations of oriented matroids, a notion of combinatorics. For the purposes of Mnëv's universality, an oriented matroid of a finite subset S ⊂...

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

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

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...

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...

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...

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

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

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

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

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. The...

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

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

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

"It seems fair to say that the major credit for the origination of oriented matroid theory should be shared by Robert Bland, Jon Folkman, Michel Las Vergnas...

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

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

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

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

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

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

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

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

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...