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arXiv · 1906.05848

Multivariate polynomials for generalized permutohedra

Eric Katz·McCabe Olsen
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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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Eric Katz, McCabe Olsen. 2019-06-13. Multivariate polynomials for generalized permutohedra. https://arxiv.org/abs/1906.05848

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