# Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs

Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs 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 (x 1, . . . , x d ) satisfying x i +  x j $${\leq}$$ ≤ 1 for every edge (i, j) of G. In this paper we show that (i) the $${\delta}$$ δ -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 $${\delta}$$ δ -vector of 2FRAC(G). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Combinatorics Springer Journals

# Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs

, Volume 22 (3) – Jun 5, 2018
11 pages

/lp/springer_journal/ehrhart-series-of-fractional-stable-set-polytopes-of-finite-graphs-BwHbQJH0b6
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Combinatorics
ISSN
0218-0006
eISSN
0219-3094
D.O.I.
10.1007/s00026-018-0392-2
Publisher site
See Article on Publisher Site

### 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 (x 1, . . . , x d ) satisfying x i +  x j $${\leq}$$ ≤ 1 for every edge (i, j) of G. In this paper we show that (i) the $${\delta}$$ δ -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 $${\delta}$$ δ -vector of 2FRAC(G).

### Journal

Annals of CombinatoricsSpringer Journals

Published: Jun 5, 2018

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