Triangulations of simplices with vanishing local h-polynomial
Combinatorics
2025-01-07 v2
Abstract
Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of triangulations of simplices whose local h-polynomial vanishes. As a first step, we identify a class of refinements that preserve the local h-polynomial. In dimensions 2 and 3, we show that all triangulations with vanishing local h-polynomial are obtained from one or two simple examples by a sequence of such refinements. In higher dimensions, we prove some partial results and give further examples.
Keywords
Cite
@article{arxiv.1909.10843,
title = {Triangulations of simplices with vanishing local h-polynomial},
author = {André de Moura and Elijah Gunther and Sam Payne and Jason Schuchardt and Alan Stapledon},
journal= {arXiv preprint arXiv:1909.10843},
year = {2025}
}
Comments
v2: 15 pages, 6 figures, minor expository improvements. To appear in Algebraic Combinatorics