Monomial ideals with minimal generalized Barile-Macchia resolutions
Commutative Algebra
2026-05-11 v1
Abstract
We identify several classes of monomial ideals that possess minimal generalized Barile-Macchia resolutions. These classes of ideals include generic monomial ideals, monomial ideals with linear quotients, and edge ideals of hypertrees. We also characterize connected unicyclic graphs whose edge ideals are bridge-friendly and, in particular, have minimal Barile-Macchia resolutions. Barile-Macchia and generalized Barile-Macchia resolutions are cellular resolutions and special types of Morse resolutions.
Cite
@article{arxiv.2412.11843,
title = {Monomial ideals with minimal generalized Barile-Macchia resolutions},
author = {Trung Chau and Huy Tai Ha and Aryaman Maithani},
journal= {arXiv preprint arXiv:2412.11843},
year = {2026}
}
Comments
are welcome! 17 pages