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Author Chen, Sheng ♦ Li, Nan ♦ Sam, Steven V.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2010-02-18
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Combinatorics ♦ Mathematics - Number Theory ♦ 52C07 ♦ 05A16 ♦ 11D45 ♦ 11D04 ♦ math
Abstract Let $P$ be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations $P(n) = nP$ is a quasi-polynomial in $n$. We generalize this theorem by allowing the vertices of P(n) to be arbitrary rational functions in $n$. In this case we prove that the number of lattice points in P(n) is a quasi-polynomial for $n$ sufficiently large. Our work was motivated by a conjecture of Ehrhart on the number of solutions to parametrized linear Diophantine equations whose coefficients are polynomials in $n$, and we explain how these two problems are related.
Description Reference: Trans. Amer. Math. Soc. 364 (2012), 551-569
Educational Use Research
Learning Resource Type Article
Page Count 18


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