In mathematics, a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is a polytope constructed via the bases of a matroid. Given a matroid , the matroid polytope is the convex hull of the indicator vectors of the bases of .
a matroidpolytope, also called a matroid basis polytope (or basis matroidpolytope) to distinguish it from other polytopes derived from a matroid, is...
basis elements. A matroid is called a paving matroid if all of its circuits have size at least equal to its rank. The matroidpolytope P M {\displaystyle...
In mathematics, a basis of a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent...
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n {\displaystyle n} -dimensional...
the combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic side...
the combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic side...
matroid, which are the vectors of the dual oriented matroid. Günter M. Ziegler introduces oriented matroids via convex polytopes. A standard matroid is...
hypersimplex Δ d , k {\displaystyle \Delta _{d,k}} is also the matroidpolytope for a uniform matroid with d {\displaystyle d} elements and rank k {\displaystyle...
discrete geometry. A polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions...
examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Convex polyhedra are...
\}}} This analogously generalizes the dominant of the spanning set polytope of matroids. When we only focus on the lattice points of our polymatroids we...
and the geometry of convex polytopes and polyhedra, it is by now also capable of dealing with simplicial complexes, matroids, polyhedral fans, graphs,...
affine (linear) function defined on this polytope. A linear programming algorithm finds a point in the polytope where this function has the largest (or...
semilattice, there is an analogous matroid-like structure called a semimatroid, which is a generalization of a matroid (and has the same relationship to...
matroid of M. Then Whitney's planarity criterion can be rephrased as stating that the dual matroid of a graphic matroid M is itself a graphic matroid...
neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the constraints applied to the objective function...
(graph theory), a symmetric tessellation of a closed surface Regular matroid, a matroid which can be represented over any field Regular paperfolding sequence...
generally, in any dimension, the Minkowski sum of line segments forms a polytope known as a zonotope. The original motivation for studying zonohedra is...
on matroid minors. Bertrand Guenin for a forbidden minor characterization of the weakly bipartite graphs (graphs whose bipartite subgraph polytope is...
his contributions to optimization, polyhedral computation and oriented matroid theory. Fukuda is a professor in optimization and computational geometry...
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