Multivariate polynomials for generalized permutohedra

Eric Katz, McCabe Olsen

Abstract


Using the notion of a 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 Sn-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.


Keywords


Generalized permutohedron, h-polynomial, q-analogues

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DOI: https://doi.org/10.26493/1855-3974.2044.fd1

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications