Reflexive polytopes arising from partially ordered sets and perfect graphs
Reflexive polytopes arising from partially ordered sets and perfect graphs
复制标题
由部分有序集和完美图产生的自反多面体
DOI：
10.1007/s10801-018-0817-3
复制
发表时间：
2019
影响因子：
0.8
通讯作者：
Tsuchiya Akiyoshi
中科院分区：
文献类型：
--
作者：
Hibi Takayuki;Tsuchiya Akiyoshi
具有整数分解性质的自反多面体是一类有意义的多面体。最近，从有限偏序集的序多面体和链多面体中得到了一些具有整数分解性质的自反多面体。在本文中，我们将推广这一结果。实际上，借助于Gröbner基上的代数技巧，我们将从有限偏序集的序多面体和完全图的稳定集多面体中引入一类具有整数分解性质的自反多面体。此外，这一结果将给出完美图的多面体刻画。最后，我们将研究这些自反多面体的Ehrhart-多项式。
Reflexive polytopes which have the integer decomposition property are of interest. Recently, some large classes of reflexive polytopes with integer decomposition property coming from the order polytopes and the chain polytopes of finite partially ordered sets are known. In the present paper, we will generalize this result. In fact, by virtue of the algebraic technique on Gröbner bases, new classes of reflexive polytopes with the integer decomposition property coming from the order polytopes of finite partially ordered sets and the stable set polytopes of perfect graphs will be introduced. Furthermore, the result will give a polyhedral characterization of perfect graphs. Finally, we will investigate the Ehrhart-polynomials of these reflexive polytopes.