Residues formulae for volumes and Ehrhart polynomials of convex polytopes

Details Residues formulae for volumes and Ehrhart polynomials of convex polytopes Residues formulae for volumes and Ehrhart polynomials of convex polytopes

2001-03-15

arxiv.org/abs/math/0103097v1

Mathematics

Combinatorics

81 pages, 4 figures

Scientific paper

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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