Scarf complexes of connected and path ideals
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914184815443968 |
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| author | Chau, Trung Sheng, Richie Tribone, Tim Wooton, Deborah |
| author_facet | Chau, Trung Sheng, Richie Tribone, Tim Wooton, Deborah |
| contents | The $t$-connected ideal of a graph $G$ is generated by all connected induced subgraphs of $G$ with $t$ vertices. When $t = 2$, this coincides with the usual edge ideal of the graph. Following the work of Faridi et al., we give a classification of the graphs whose $t$-connected ideals are minimally resolved by their Scarf complex. We also consider the $t$-path ideal of a graph $G$ which is the ideal generated by all paths of length $t$ in $G$. In this case, we are able to give a classification of the same type for paths of length $t = 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scarf complexes of connected and path ideals Chau, Trung Sheng, Richie Tribone, Tim Wooton, Deborah Commutative Algebra Combinatorics 13F55, 13D02 The $t$-connected ideal of a graph $G$ is generated by all connected induced subgraphs of $G$ with $t$ vertices. When $t = 2$, this coincides with the usual edge ideal of the graph. Following the work of Faridi et al., we give a classification of the graphs whose $t$-connected ideals are minimally resolved by their Scarf complex. We also consider the $t$-path ideal of a graph $G$ which is the ideal generated by all paths of length $t$ in $G$. In this case, we are able to give a classification of the same type for paths of length $t = 4$. |
| title | Scarf complexes of connected and path ideals |
| topic | Commutative Algebra Combinatorics 13F55, 13D02 |
| url | https://arxiv.org/abs/2512.05376 |