Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs

被引：0
|
作者：
Hamano, Ginji [1 ]
Hibi, Takayuki [1 ]
Ohsugi, Hidefumi [2 ]
机构：
[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, Suita, Osaka 5650871, Japan
[2] Kwansei Gakuin Univ, Sch Sci & Technol, Dept Math Sci, Sanda, Hyogo 6691337, Japan
来源：
ANNALS OF COMBINATORICS | 2018年 / 22卷 / 03期
关键词：
Ehrhart series; Ehrhart rings; fractional stable set polytopes; Gorenstein Fano polytopes; unimodal delta-vectors; VECTORS;
D O I：
10.1007/s00026-018-0392-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 xi + x j <= 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).
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页码：563 / 573
页数：11
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