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Matroid polytope : ウィキペディア英語版
Matroid polytope
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 M, the matroid polytope P_M is the convex hull of the indicator vectors of the bases of M.
==Definition==
Let M be a matroid on n elements. Given a basis B \subseteq \ of M, the indicator vector of B is
:\mathbf e_B := \sum_ \mathbf e_i,
where \mathbf e_i is the standard ith unit vector in \mathbb^n. The matroid polytope P_M is the convex hull of the set
:\ \subseteq \mathbb^n.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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