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Annals of Combinatorics

, Volume 22, Issue 3, pp 563–573 | Cite as

Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs

  • Ginji Hamano
  • Takayuki Hibi
  • Hidefumi Ohsugi
Article
  • 41 Downloads

Abstract

The fractional stable set polytope FRAC(G) of a simple graph G with d vertices is a rational polytope that is the set of nonnegative vectors (x1, . . . , xd) satisfying xixj \({\leq}\) 1 for every edge (i, j) of G. In this paper we show that (i) the \({\delta}\)-vector of a lattice polytope 2FRAC(G) is alternatingly increasing, (ii) the Ehrhart ring of FRAC(G) is Gorenstein, (iii) the coefficients of the numerator of the Ehrhart series of FRAC(G) are symmetric, unimodal and computed by the \({\delta}\)-vector of 2FRAC(G).

Mathematics Subject Classification

52B05 52B20 

Keywords

Ehrhart series Ehrhart rings fractional stable set polytopes Gorenstein Fano polytopes unimodal \({\delta}\)-vectors 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Pure and Applied Mathematics, Graduate School of Information Science and TechnologyOsaka UniversitySuitaJapan
  2. 2.Department of Mathematical Sciences, School of Science and TechnologyKwansei Gakuin UniversitySandaJapan

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