Maximal Periods of (Ehrhart) Quasi-Polynomials
| dc.creator | Beck, Matthias | |
| dc.creator | Sam, Steven | |
| dc.creator | Woods, Kevin | |
| dc.date | 2007-02-09 | |
| dc.date | 2007-08-17 | |
| dc.date.accessioned | 2026-07-07T09:24:07Z | |
| dc.date.available | 2026-07-07T09:24:07Z | |
| dc.description | A \emph{quasi-polynomial} is a function defined of the form $q(k) = c_d(k) k^d + c_{d-1}(k) k^{d-1} + ... + c_0(k)$, where $c_0, c_1, ..., c_d$ are periodic functions in $k \in \Z$. Prominent examples of quasi-polynomials appear in Ehrhart's theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the $c_j(k)$ for Ehrhart quasi-polynomials. For generic polytopes, McMullen's bounds seem to be sharp, but sometimes smaller periods exist. We prove that the second leading coefficient of an Ehrhart quasi-polynomial always has maximal expected period and present a general theorem that yields maximal periods for the coefficients of certain quasi-polynomials. We present a construction for (Ehrhart) quasi-polynomials that exhibit maximal period behavior and use it to answer a question of Zaslavsky on convolutions of quasi-polynomials. | |
| dc.description | 7 pages, to appear in JCT-A | |
| dc.identifier | https://arxiv.org/abs/math/0702242 | |
| dc.identifier | http://arxiv.org/abs/math/0702242 | |
| dc.identifier | J. Combin. Theory Ser. A 115, no. 3 (2008), 517-525 | |
| dc.identifier | doi:10.1016/j.jcta.2007.05.009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155982 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15; 52C07 | |
| dc.title | Maximal Periods of (Ehrhart) Quasi-Polynomials | |
| dc.type | text |