Periods of Ehrhart coefficients of rational polytopes
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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.
@article{10_37236_6059,
author = {Tyrrell B. McAllister and H\'el\`ene O. Rochais},
title = {Periods of {Ehrhart} coefficients of rational polytopes},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/6059},
zbl = {arXiv:2601.22992},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6059/}
}
Tyrrell B. McAllister; Hélène O. Rochais. Periods of Ehrhart coefficients of rational polytopes. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6059
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