Minimal Cellular Resolutions of Path Ideals
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909548102549504 |
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| 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 |
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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 |