A bijective proof for a theorem of Ehrhart

Details A bijective proof for a theorem of Ehrhart A bijective proof for a theorem of Ehrhart

2008-01-29

arxiv.org/abs/0801.4432v5

Amer. Math. Monthly 116 (2009), no. 8, 688-701

Mathematics

Combinatorics

14 pages, 4 figures; v5: polished exposition, final version

Scientific paper

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.

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