q-analogues of Ehrhart polynomials

Frédéric Chapoton (1)

1 ICJ - Institut Camille Jordan

One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q^f(v) for some linear form f. One proposes a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the q-integers.

On introduit un q-analogue de la théorie classique des polynômes d'Ehrhart, qui fait intervenir l'évaluation en les q-entiers. On étudie en particulier le cas des polytopes associés aux ordres partiels et le cas des polytopes vides.

Mots clés: q-integer; ehrhart series; ehrhart polynomial; polytope

Domaines: Algèbres quantiques [math.QA]

Frédéric Chapoton. q-analogues of Ehrhart polynomials. Proceedings of the Edinburgh Mathematical Society, 2015, ⟨10.1017/S0013091515000243⟩. ⟨hal-00771665v2⟩