English

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.

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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}
}

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14 pages