The face vector of a half-open hypersimplex

Abstract

The half-open hypersimplex ${\Delta }_{n,k}^{\prime }$ consists of those $x=(x_1,\dots ,x_n)\in [0,1{]}^n$ with $k-1<x_1+\cdots +x_n\le k$, where $0<k\le n$. The $f$-vector of a half-open hypersimplex and related generating functions are explicitly studied.

9 pages

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