Name
Abstract | ||
|---|---|---|
A quasi-polynomial is a function defined of the form q(k)=cd(k)kd+cd−1(k)kd−1+⋯+c0(k), where c0,c1,…,cd are periodic functions in k∈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 cj(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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.jcta.2007.05.009 | Journal of Combinatorial Theory, Series A |
Keywords | DocType | Volume |
Ehrhart quasi-polynomial,Period,Lattice points,Rational polytope,Quasi-polynomial convolution | Journal | 115 |
Issue | ISSN | Citations |
3 | 0097-3165 | 8 |
PageRank | References | Authors |
0.81 | 5 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Matthias Beck | 1 | 54 | 10.27 |
| Steven V. Sam | 2 | 20 | 4.36 |
| Kevin M. Woods | 3 | 25 | 6.04 |