Ehrhart-Macdonald reciprocity extended

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
9 pages, 1 figure

Keywords

Combinatorics, 52C07; 05A15

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/74866

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504230
 http://arxiv.org/abs/math/0504230

Collections

arXiv