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.
@article{10_37236_12970,
author = {Trung Chau and Selvi Kara and Wang Kyle},
title = {Minimal cellular resolutions of path ideals},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {4},
doi = {10.37236/12970},
zbl = {8120109},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12970/}
}
TY - JOUR
AU - Trung Chau
AU - Selvi Kara
AU - Wang Kyle
TI - Minimal cellular resolutions of path ideals
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/12970/
DO - 10.37236/12970
ID - 10_37236_12970
ER -
%0 Journal Article
%A Trung Chau
%A Selvi Kara
%A Wang Kyle
%T Minimal cellular resolutions of path ideals
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12970/
%R 10.37236/12970
%F 10_37236_12970
Trung Chau; Selvi Kara; Wang Kyle. Minimal cellular resolutions of path ideals. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/12970
