English

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.

Keywords

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

R2 v1 2026-06-28T20:37:09.650Z