A bijective proof for a theorem of Ehrhart

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.

arXiv comment14 pages, 4 figures; v5: polished exposition, final version