Interpreting the Ehrhart coefficients of cross-polytopes
Combinatorics
2025-12-10 v1
Abstract
It is known that the Ehrhart polynomials of cross-polytopes, as well as of pyramids over them, have positive coefficients. We give a combinatorial proof of this fact by showing that a scaled version of the Ehrhart polynomials are generating functions for certain colored permutations. This answers a question posed by Stanley.
Keywords
Cite
@article{arxiv.2512.08669,
title = {Interpreting the Ehrhart coefficients of cross-polytopes},
author = {Krishna Menon and Emil Verkama},
journal= {arXiv preprint arXiv:2512.08669},
year = {2025}
}
Comments
14 pages