Residue formulae, vector partition functions and lattice points in rational polytopes

Brion, Michel; Vergne, Michèle

doi:10.1090/S0894-0347-97-00242-7

Residue formulae, vector partition functions and lattice points in rational polytopes
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by Michel Brion and Michèle Vergne

J. Amer. Math. Soc. 10 (1997), 797-833

DOI: https://doi.org/10.1090/S0894-0347-97-00242-7

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Abstract:

We obtain residue formulae for certain functions of several variables. As an application, we obtain closed formulae for vector partition functions and for their continuous analogs. They imply an Euler-MacLaurin summation formula for vector partition functions, and for rational convex polytopes as well: we express the sum of values of a polynomial function at all lattice points of a rational convex polytope in terms of the variation of the integral of the function over the deformed polytope.

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