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Arzu Boysal; Michèle Vergne
Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator
(Les formules de saut de Paradan pour les fonctions de partitions, et opérateurs de Khovanski-Pukhlikov)
Annales de l'institut Fourier, 59 no. 5 (2009), p. 1715-1752, doi: 10.5802/aif.2475
Article PDF | Reviews MR 2573189 | Zbl 1186.52006 | 1 citation in Cedram
Class. Math.: 52B20, 14M25
Keywords: Polytopes, toric varieties

Résumé - Abstract

Let $P(s)$ be a family of rational polytopes parametrized by inequations. It is known that the volume of $P(s)$ is a locally polynomial function of the parameters. Similarly, the number of integral points in $P(s)$ is a locally quasi-polynomial function of the parameters. Paul-Émile Paradan proved a jump formula for this function, when crossing a wall. In this article, we give an algebraic proof of this formula. Furthermore, we give a residue formula for the jump, which enables us to compute it.

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