Local h∗-polynomials for one-row Hermite normal form simplices

Bajo, Esme; Braun, Benjamin; Codenotti, Giulia; Hofscheier, Johannes; Vindas-Meléndez, Andrés R.

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.

Citation

Bajo, E., Braun, B., Codenotti, G., Hofscheier, J., & Vindas-Meléndez, A. R. (2025). Local h∗-polynomials for one-row Hermite normal form simplices. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, https://doi.org/10.1007/s13366-025-00784-z

• Journal Article Type: Article
• Acceptance Date: Jan 7, 2025
• Online Publication Date: Feb 9, 2025
• Publication Date: Feb 9, 2025
• Deposit Date: Feb 13, 2025
• Publicly Available Date: Feb 10, 2026
• Journal: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• Print ISSN: 0138-4821
• Electronic ISSN: 2191-0383
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1007/s13366-025-00784-z
• Public URL: https://nottingham-repository.worktribe.com/output/45311587
• Publisher URL: https://link.springer.com/article/10.1007/s13366-025-00784-z