The $h$-vectors of toric ideals of odd cycle compositions revisited

Fuente: arXiv
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Autori principali: Bhaskara, Kieran, Van Tuyl, Adam, Zotine, Sasha
Natura: Preprint
Pubblicazione: 2025
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author Bhaskara, Kieran
Van Tuyl, Adam
Zotine, Sasha
author_facet Bhaskara, Kieran
Van Tuyl, Adam
Zotine, Sasha
contents Let $G$ be a graph consisting of $s$ odd cycles that all share a common vertex. Bhaskara, Higashitani, and Shibu Deepthi recently computed the $h$-polynomial for the quotient ring $R/I_G$, where $I_G$ is the toric ideal of $G$, in terms of the number and sizes of odd cycles in the graph. The purpose of this note is to prove the stronger result that these toric ideals are geometrically vertex decomposable, which allows us to deduce the result of Bhaskara, Higashitani, and Shibu Deepthi about the $h$-polyhomial as a corollary.
format Preprint
id arxiv_https___arxiv_org_abs_2504_13087
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The $h$-vectors of toric ideals of odd cycle compositions revisited
Bhaskara, Kieran
Van Tuyl, Adam
Zotine, Sasha
Commutative Algebra
Combinatorics
13D02, 13D40, 13P10, 13F65, 14M25, 05E40
Let $G$ be a graph consisting of $s$ odd cycles that all share a common vertex. Bhaskara, Higashitani, and Shibu Deepthi recently computed the $h$-polynomial for the quotient ring $R/I_G$, where $I_G$ is the toric ideal of $G$, in terms of the number and sizes of odd cycles in the graph. The purpose of this note is to prove the stronger result that these toric ideals are geometrically vertex decomposable, which allows us to deduce the result of Bhaskara, Higashitani, and Shibu Deepthi about the $h$-polyhomial as a corollary.
title The $h$-vectors of toric ideals of odd cycle compositions revisited
topic Commutative Algebra
Combinatorics
13D02, 13D40, 13P10, 13F65, 14M25, 05E40
url https://arxiv.org/abs/2504.13087