Minimal Cellular Resolutions of Path Ideals
Commutative Algebra
2025-03-25 v3 Combinatorics
Abstract
In this paper, we prove that the path ideals of both paths and cycles have minimal cellular resolutions. Specifically, these minimal free resolutions coincide with the Barile-Macchia resolutions for paths, and their generalized counterparts for cycles. Furthermore, we identify edge ideals of cycles as a class of ideals that lack a minimal Barile-Macchia resolution, yet have a minimal generalized Barile-Macchia resolution.
Cite
@article{arxiv.2403.16324,
title = {Minimal Cellular Resolutions of Path Ideals},
author = {Trung Chau and Selvi Kara and Kyle Wang},
journal= {arXiv preprint arXiv:2403.16324},
year = {2025}
}
Comments
22 pages, references and the introduction are updated with 2 new references. March 2025 revision includes expanded proofs