Ehrhart-Macdonald reciprocity extended

Details Ehrhart-Macdonald reciprocity extended Ehrhart-Macdonald reciprocity extended

2005-04-11

arxiv.org/abs/math/0504230v1

Mathematics

Combinatorics

9 pages, 1 figure

Scientific paper

For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an intimate relation between these two counting functions. A similar counting function and reciprocity law exists for the sum of all solid angles at integer points in dilates of P. We derive a unifying generalization of these reciprocity theorems which follows in a natural way from Brion's Theorem on conic decompositions of polytopes.

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