2021
DOI: 10.48550/arxiv.2103.09073
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Pruned inside-out polytopes, combinatorial reciprocity theorems and generalized permutahedra

Abstract: Generalized permutahedra are a class of polytopes with many interesting combinatorial subclasses. We introduce pruned inside-out polytopes, a generalization of inside-out polytopes introduced by Beck-Zaslavsky ( 2006), which have many applications such as recovering the famous reciprocity result for graph colorings by Stanley. We study the integer point count of pruned inside-out polytopes by applying classical Ehrhart polynomials and Ehrhart-Macdonald reciprocity. This yields a geometric perspective on and a … Show more

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