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Integer decomposition property for Cayley sums of order and stable set polytopes. (arXiv:1807.05989v1 [math.CO])
来源于:arXiv
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. 查看全文>>