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arXiv · 2403.16324

Minimal Cellular Resolutions of Path Ideals

Trung Chau·Selvi Kara·Kyle Wang
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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.

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Trung Chau, Selvi Kara, Kyle Wang. 2024-03-24. Minimal Cellular Resolutions of Path Ideals. https://arxiv.org/abs/2403.16324

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