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arXiv · 1603.09613

Ehrhart series of fractional stable set polytopes of finite graphs

Ginji Hamano·Takayuki Hibi·Hidefumi Ohsugi
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Abstract

The fractional stable set polytope ${\rm FRAC}(G)$ of a simple graph $G$ with $d$ vertices is a rational polytope that is the set of nonnegative vectors $(x_1,\ldots,x_d)$ satisfying $x_i+x_j\le 1$ for every edge $(i,j)$ of $G$. In this paper we show that (i) The $\delta$-vector of a lattice polytope $2 {\rm FRAC}(G)$ is alternatingly increasing; (ii) The Ehrhart ring of ${\rm FRAC}(G)$ is Gorenstein; (iii) The coefficients of the numerator of the Ehrhart series of ${\rm FRAC}(G)$ are symmetric, unimodal and computed by the $\delta$-vector of $2 {\rm FRAC}(G)$.

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Ginji Hamano, Takayuki Hibi, Hidefumi Ohsugi. 2016-03-31. Ehrhart series of fractional stable set polytopes of finite graphs. https://doi.org/10.1007/s00026-018-0392-2

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