# Category: Oriented matroids

Oriented matroid
An oriented matroid is a mathematical structure that abstracts the properties of directed graphs, vector arrangements over ordered fields, and hyperplane arrangements over ordered fields. In compariso
Krein–Milman theorem
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem — A comp
Mnëv's universality theorem
In algebraic geometry, Mnëv's universality theorem is a result which can be used to represent algebraic (or semi algebraic) varieties as realizations of oriented matroids, a notion of combinatorics.
Signed graph
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is
In mathematical optimization, Zadeh's rule (also known as the least-entered rule) is an algorithmic refinement of the simplex method for linear optimization. The rule was proposed around 1980 by Norma
Arrangement of hyperplanes
In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A g
Criss-cross algorithm
In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear ineq
Zonohedron
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). Any zonohedron may equivalently be described as
Bland's rule
In mathematical optimization, Bland's rule (also known as Bland's algorithm, Bland's anti-cycling rule or Bland's pivot rule) is an algorithmic refinement of the simplex method for linear optimization
Cunningham's rule
In mathematical optimization, Cunningham's rule (also known as least recently considered rule or round-robin rule) is an algorithmic refinement of the simplex method for linear optimization. The rule
CC system
In computational geometry, a CC system or counterclockwise system is a ternary relation pqr introduced by Donald Knuth to model the clockwise ordering of triples of points in general position in the E