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
Japan

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

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

Abstract:

The half-open hypersimplex Δ'n,k consists of those (x1, ..., xn) ∈ [0,1]n with k - 1 < x1 + ... + xn ≤ k, where 0 < k ≤ n. 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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