Periods of Ehrhart coefficients of rational polytopes
type: Item
instance of: scholarly article
title: Periods of Ehrhart coefficients of rational polytopes
zbMATH Open document ID: 1390.52016
author: Tyrrell B. McAllister
author: Hélène O. Rochais
published in: The Electronic Journal of Combinatorics
publication date: 2018-05-25T00:00:00Z
full work available at URL: v25i1p64
review text: Summary: Let \(\mathcal{P} \subset \mathbb{R}^{n}\) be a polytope whose vertices have rational coordinates. By a seminal result of E. Ehrhart, the number of integer lattice points in the \(k\)th dilate of \(\mathcal{P}\) (\(k\) a positive integer) is a quasi-polynomial function of \(k\) -- that is, a ``polynomial'' in which the coefficients are themselves periodic functions of \(k\). It is an open problem to determine which quasi-polynomials are the Ehrhart quasi-polynomials of rational polytopes. As partial progress on this problem, we construct families of polytopes in which the periods of the coefficient functions take on various prescribed values.
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 52B20
zbMATH DE Number: 6873108
zbMATH Keywords: rational polytopes
zbMATH Keywords: Ehrhart quasi-polynomials
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6873108