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

2025/04/17 by Bhaskara, Kieran, Van Tuyl, Adam, Zotine, Sasha
#05E40 #13D02 #13D40 #13F65 #13P10 #14M25 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.13087

Abstract

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.

Citations

• h-vectors of edge rings of odd-cycle compositions
• Root polytopes, tropical types, and toric edge ideals
• The h-vectors of the edge rings of a special family of graphs
• Geometric vertex decomposition and liaison for toric ideals of graphs
• Algebraic properties of toric rings of graphs
• Bounds on the regularity of toric ideals of graphs
• Depth of edge rings arising from finite graphs
• Gröbner geometry of vertex decompositions and of flagged tableaux

Related

• h-vectors of edge rings of odd-cycle compositions
• Regularity and h-polynomials of toric ideals of graphs
• Geometric vertex decomposition and liaison for toric ideals of graphs
• A note on toric ideals of graphs and Knutson-Miller-Yong decompositions
• Toric rings arising from vertex cover ideals