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


Authors: Michel Brion and Michèle Vergne
Journal: J. Amer. Math. Soc. 10 (1997), 797-833
MSC (1991): Primary 11P21, 52B20
DOI: https://doi.org/10.1090/S0894-0347-97-00242-7
MathSciNet review: 1446364
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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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Additional Information

Michel Brion
Affiliation: Institut Fourier, B.P. 74, 38402 Saint-Martin d’Hères Cedex, France
Email: mbrion@fourier.ujf-grenoble.fr

Michèle Vergne
Affiliation: École Normale Supérieure, 45 rue d’Ulm, 75005 Paris Cedex 05, France
Email: vergne@dmi.ens.fr

DOI: https://doi.org/10.1090/S0894-0347-97-00242-7
Keywords: Vector partition functions, rational convex polytopes
Received by editor(s): December 30, 1996
Received by editor(s) in revised form: March 28, 1997
Article copyright: © Copyright 1997 American Mathematical Society

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