Multivariate polynomials for generalized permutohedra

2019/06/13 by Katz, Eric, Olsen, McCabe
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.05848

Abstract

Using the notion of Mahonian statistic on acyclic posets, we introduce a q-analogue of the h-polynomial of a simple generalized permutohedron. We focus primarily on the case of nestohedra and on explicit computations for many interesting examples, such as S_n-invariant nestohedra, graph associahedra, and Stanley--Pitman polytopes. For the usual (Stasheff) associahedron, our generalization yields an alternative q-analogue to the well-studied Narayana numbers.

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