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Hypersimplex : ウィキペディア英語版
Hypersimplex

In polyhedral combinatorics, a hypersimplex, Δ''d'',''k'', is a convex polytope that generalizes the simplex. It is determined by two parameters ''d'' and ''k'', and is defined as the convex hull of the ''d''-dimensional vectors whose coefficients consist of ''k'' ones and ''d'' − ''k'' zeros. It forms a (''d'' − 1)-dimensional polytope, because all of these vectors lie in a single (''d'' − 1)-dimensional hyperplane.〔.〕
==Properties==
The number of vertices in Δ''d'',''k'' is \tbinom.〔
The graph formed by the vertices and edges of a hypersimplex Δ''d'',''k'' is the Johnson graph ''J''(''d'',''k'').〔.〕

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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