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.
| Original language | English |
|---|---|
| Pages (from-to) | 1065-1099 |
| Number of pages | 35 |
| Journal | Beitrage zur Algebra und Geometrie |
| Volume | 66 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2025 |
Bibliographical note
Publisher Copyright:© The Managing Editors 2025.
Funding
The authors thank the anonymous referee for their helpful comments. The authors thank the American Institute of Mathematics, where this project was started as a result of the workshop “Ehrhart polynomials: inequalities and extremal constructions.” The authors also thank Ahmed Umer Ashraf, Matthias Beck, and Marie Meyer for helpful conversations at the start of this project. Andrés R. Vindas-Meléndez was partially supported by the National Science Foundation under Award DMS-2102921. Benjamin Braun is partially supported by the National Science Foundation under award DMS-1953785. The authors thank the anonymous referee for their helpful comments. The authors thank the American Institute of Mathematics, where this project was started as a result of the workshop “Ehrhart polynomials: inequalities and extremal constructions.” The authors also thank Ahmed Umer Ashraf, Matthias Beck, and Marie Meyer for helpful conversations at the start of this project. Andrés R. Vindas-Meléndez was partially supported by the National Science Foundation under Award DMS-2102921. Benjamin Braun is partially supported by the National Science Foundation under award DMS-1953785.
| Funders | Funder number |
|---|---|
| Marie Meyer | |
| American Institute of Mathematics Structured Quartet Research Ensembles | |
| National Science Foundation Arctic Social Science Program | DMS-2102921, DMS-1953785 |
Keywords
- Ehrhart theory
- Hermite normal form
- Lattice simplex
- Unimodal
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology