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Lecture 2 Residue Formulae For Volumes And Number Of Integral Points In Convex Rational Polytopes

In: European Women In Mathematics

Author

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  • MICHÈLE VERGNE

    (Centre de Mathematiques, Ecole Polytechnique, F-91128 Palaiseau Cedex, France)

Abstract

We first discuss here some classical results on the number of points with integral coordinates in convex rational polytopes P ⊂ Rn starting with Ehrhart's theorem. Then, following Baldoni-Vergne and Szenes-Vergne, we present some recent results giving number of points with integral coordinates in P in terms of multidimensional residues. In particular, this allows to recover relations established by Khovanskii-Pukhlikov, Cappell-Shaneson and Brion-Vergne between volumes and number of points with integral coordinates in families of polytopes with parallel facets.

Suggested Citation

  • Michèle Vergne, 2003. "Lecture 2 Residue Formulae For Volumes And Number Of Integral Points In Convex Rational Polytopes," World Scientific Book Chapters, in: Emilia Mezzetti & Sylvie Paycha (ed.), European Women In Mathematics, chapter 14, pages 245-285, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812704276_0014
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