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Computing the period of an Ehrhart quasi-polynomial | | Kevin M. Woods
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9 Nov 2004 | | Subject: | Combinatorics | math.CO | | Abstract: | If P is a rational polytope in R^d, then $i_P(t):=#(tPcap Z^d)$ is a quasi-polynomial in t, called the Ehrhart quasi-polynomial of P. A period of i_P(t) is D(P), the smallest positive integer D such that D*P has integral vertices. Often, D(P) is the minimum period of i_P(t), but, in several interesting examples, the minimum period is smaller. We prove that, for fixed d, there is a polynomial time algorithm which, given a rational polytope P in R^d and an integer n, decides whether n is a period of i_P(t). In particular, there is a polynomial time algorithm to decide whether i_P(t) is a polynomial. We conjecture that, for fixed d, there is a polynomial time algorithm to compute the minimum period of i_P(t). The tools we use are rational generating functions. | | Source: | arXiv, math.CO/0411207 | | Services: | Forum | Review | PDF | Favorites | |
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