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q-analogues of Ehrhart polynomials

Published online by Cambridge University Press:  17 December 2015

F. Chapoton
F. Chapoton*
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, Bâtiment Braconnier, 21 Avenue Claude Bernard, 69622 Villeurbanne Cedex, France (chapoton@math.univ-lyon1.fr)
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Abstract

We consider weighted sums over points of lattice polytopes, where the weight of a point v is the monomial qλ(v) for some linear form λ. We propose a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the q-integers. The main novelty is the proposal to consider q-Ehrhart polynomials. This general theory is then applied to the special case of order polytopes associated with partially ordered sets. Some more specific properties are described in the case of empty polytopes.

Keywords

lattice polytopesq-analogueEhrhart polynomialposetPrimary 52B2006A11
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 339 - 358
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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