English

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.

Keywords

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

R2 v1 2026-06-21T10:07:25.225Z