Integer Decomposition Property for Cayley Sums of Order and Stable Set Polytopes
Integer Decomposition Property for Cayley Sums of Order and Stable Set Polytopes
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DOI：
10.1307/mmj/1585792887
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发表时间：
2018-07
影响因子：
0.9
通讯作者：
T. Hibi;Hidefumi Ohsugi;Akiyoshi Tsuchiya
中科院分区：
文献类型：
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作者：
T. Hibi;Hidefumi Ohsugi;Akiyoshi Tsuchiya
具有整数分解性质的格多面体出现在数学的许多领域。已知如果格多面体的Cayley和具有IDP，则它们的Minkowski和也具有IDP。本文研究了有限偏序集的序多面体与有限简单图的稳定集多面体的Cayley和。证明了序多面体的Cayley和与完美图的稳定集多面体的Cayley和具有正则幺模三角剖分和IDP，从而它们的Minkowski和也具有正则幺模三角剖分和IDP。此外，证明了对于图的序多面体和稳定集多面体，下列条件是等价的：（i）Cayley和是Gorenstein;（ii）Minkowski和是Gorenstein;（iii）图是完美的。
Lattice polytopes which possess the integer decomposition property (IDP for short) turn up in many fields of mathematics. It is known that if the Cayley sum of lattice polytopes possesses IDP, then so does their Minkowski sum. In this paper, the Cayley sum of the order polytope of a finite poset and the stable set polytope of a finite simple graph is studied. We show that the Cayley sum of an order polytope and the stable set polytope of a perfect graph possesses a regular unimodular triangulation and IDP, and hence so does their Minkowski sum. Moreover, it turns out that, for an order polytope and the stable set polytope of a graph, the following conditions are equivalent: (i) the Cayley sum is Gorenstein; (ii) the Minkowski sum is Gorenstein; (iii) the graph is perfect.