2005/04/11 by Matthias Beck, Beck, Matthias, Richard Ehrenborg +1
Mathematics · #Advanced Combinatorial Mathematics #math.CO #msc:05A15 #msc:52C07
paper · pdf · doi:10.48550/arxiv.math/0504230
9 pages, 1 figure
arxiv created 2005/04/11 · arxiv updated 2009/12/01
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.