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Minimal Cellular Resolutions of Path Ideals

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arxiv 2403.16324 v3 pith:4Z5E2MDV submitted 2024-03-24 math.AC math.CO

Trung Chau , Selvi Kara , Kyle Wang This is my paper · ORCID
classification math.ACmath.CO
keywords minimalidealsresolutionsbarile-macchiacyclescellulargeneralizedpath
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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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  1. Minimal cellular resolutions of monomial ideals with five generators and their Artinian reductions

    math.AC 2025-02 conditional novelty 4.0 of 10

    Monomial ideals with at most five generators and their Artinian reductions have minimal generalized Barile-Macchia resolutions, and hence minimal cellular resolutions.

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