Minimal Cellular Resolutions of Path Ideals

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Chau, Trung, Kara, Selvi, Wang, Kyle
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909548102549504
author Chau, Trung
Kara, Selvi
Wang, Kyle
author_facet Chau, Trung
Kara, Selvi
Wang, Kyle
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_16324
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Minimal Cellular Resolutions of Path Ideals
Chau, Trung
Kara, Selvi
Wang, Kyle
Commutative Algebra
Combinatorics
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.
title Minimal Cellular Resolutions of Path Ideals
topic Commutative Algebra
Combinatorics
url https://arxiv.org/abs/2403.16324