Residues formulae for volumes and Ehrhart polynomials of convex polytopes

2001/03/15 by Welleda Baldoni-Silva, Baldoni-Silva, Welleda, Michèle Vergne +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0103097

81 pages, 4 figures

arxiv created 2001/03/15 · arxiv updated 2019/08/15

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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