Periods of Ehrhart coefficients of rational polytopes
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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Zbl DOI arXiv
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.
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
@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/}
}
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