Cellular resolutions of second powers of square-free monomial ideals with divisibility relations
Commutative Algebra
2026-05-22 v1 Combinatorics
Abstract
Using divisibility relations between the generators of a square-free monomial ideal , we describe divisibility relations between the generators of the second power . We then employ discrete Morse theory to produce a cellular free resolution of which is minimal for specific ideals that are extremal with respect to a given divisibility relation. In particular, we provide sharp bounds on the projective dimension of when the generators of satisfy at least one divisibility relation.
Keywords
Cite
@article{arxiv.2605.22280,
title = {Cellular resolutions of second powers of square-free monomial ideals with divisibility relations},
author = {Susan M. Cooper and Sabine El Khoury and Sara Faridi and Susan Morey and Liana M. Sega and Sandra Spiroff},
journal= {arXiv preprint arXiv:2605.22280},
year = {2026}
}