Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.6

The Face Vector of a Half-Open Hypersimplex

Takayuki Hibi
Department of Pure and Applied Mathematics
Graduate School of Information Science and Technology
Osaka University
Toyonaka, Osaka 560-0043

Nan Li
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139

Hidefumi Ohsugi
Department of Mathematical Sciences
School of Science and Technology
Kwansei Gakuin University Sanda, Hyogo, 669-1337


The half-open hypersimplex Δ'n,k consists of those (x1, ..., xn) ∈ [0,1]n with k - 1 < x1 + ... + xnk, where 0 < kn. In this paper, we study the f-vector of a half-open hypersimplex and its generating functions.

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Received October 13 2014; revised version received May 29 2015. Published in Journal of Integer Sequences, June 3 2015.

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