Degree of $h$-polynomials of edge ideals
Commutative Algebra
2024-08-26 v2
Abstract
In this paper, we investigate the degree of -polynomials of edge ideals of finite simple graphs. In particular, we provide combinatorial formulas for the degree of the -polynomial for various fundamental classes of graphs such as paths, cycles, and bipartite graphs. To the best of our knowledge, this marks the first investigation into the combinatorial interpretation of this algebraic invariant. Additionally, we characterize all connected graphs in which the sum of the Castelnuovo-Mumford regularity and the degree of the -polynomial of an edge ideal reaches its maximum value, which is the number of vertices in the graph.
Cite
@article{arxiv.2408.12544,
title = {Degree of $h$-polynomials of edge ideals},
author = {Jennifer Biermann and Selvi Kara and Augustine O'Keefe and Joseph Skelton and Gabriel Sosa},
journal= {arXiv preprint arXiv:2408.12544},
year = {2024}
}
Comments
19 pages, 7 figures