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arXiv · 2309.01186

Local $h^*$-polynomials for one-row Hermite normal form simplices

Esme Bajo·Benjamin Braun·Giulia Codenotti·Johannes Hofscheier·Andrés R. Vindas-Meléndez
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Abstract

The local $h^*$-polynomial of a lattice polytope is an important invariant arising in Ehrhart theory. Our focus is on lattice simplices presented in Hermite normal form with a single non-trivial row. We prove that when the off-diagonal entries are fixed, the distribution of coefficients for the local $h^*$-polynomial of these simplices has a limit as the normalized volume goes to infinity. Further, this limiting distribution is determined by the coefficients for a particular choice of normalized volume. We also provide an analysis of two specific families of such simplices to illustrate and motivate our main result.

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Esme Bajo, Benjamin Braun, Giulia Codenotti, Johannes Hofscheier, Andrés R. Vindas-Meléndez. 2023-09-03. Local $h^*$-polynomials for one-row Hermite normal form simplices. https://arxiv.org/abs/2309.01186

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