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Residues formulae for volumes and Ehrhart polynomials of convex polytopes

Welleda Baldoni-Silva·Michèle Vergne
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Abstract

In these notes, we explain residue formulae for volumes of convex polytopes, and for Ehrahrt polynomials based on the notion of total residue. We apply this method to the computation of the volume of the Chan-Robbins polytope. The final computation is based on a total residue formula for the system $A_n$, similar to Morris identity. For flow polytopes, a formula of change of variables in total residues leads to a "nice formula" for Ehrhart polynomials in function of mixed volumes. We apply it to Pitman-Stanley polytope.

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Welleda Baldoni-Silva, Michèle Vergne. 2001-03-15. Residues formulae for volumes and Ehrhart polynomials of convex polytopes. https://arxiv.org/abs/math/0103097

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