h -完美图稳定集多面体的ehrhart环的gorenstein性质

IF 0.5 Q3 MATHEMATICS International Electronic Journal of Algebra Pub Date : 2020-05-07 DOI:10.24330/IEJA.969935

Mitsuhiro Miyazaki

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引用次数: 10

摘要

本文给出了h-完美图的稳定集多面体的Ehrhart环的Gorenstein性质的一个判据:h-完美图$G$的稳定集多多体的Ehrhart环是Gorenstein的当且仅当(1)最大团的大小恒定(如$n$)， (2) (a) $n=1$， (b) $n=2$且不存在无弦且长度至少为7的奇环或(c) $n\geq 3$且不存在无弦且长度至少为5的奇环。

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ON THE GORENSTEIN PROPERTY OF THE EHRHART RING OF THE STABLE SET POLYTOPE OF AN H-PERFECT GRAPH

In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes of maximal cliques are constant (say $n$) and (2) (a) $n=1$, (b) $n=2$ and there is no odd cycle without chord and length at least 7 or (c) $n\geq 3$ and there is no odd cycle without chord and length at least 5.

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来源期刊

International Electronic Journal of Algebra MATHEMATICS-

CiteScore

0.90

自引率

16.70%

发文量

审稿时长

36 weeks

期刊介绍： The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.

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