A bijective proof for a theorem of Ehrhart
Combinatorics
2012-12-27 v5
Abstract
We give a new proof for a theorem of Ehrhart regarding the quasi-polynomiality of the function that counts the number of integer points in the integral dilates of a rational polytope. The proof involves a geometric bijection, inclusion-exclusion, and recurrence relations, and we also prove Ehrhart reciprocity using these methods.
Cite
@article{arxiv.0801.4432,
title = {A bijective proof for a theorem of Ehrhart},
author = {Steven V Sam},
journal= {arXiv preprint arXiv:0801.4432},
year = {2012}
}
Comments
14 pages, 4 figures; v5: polished exposition, final version