Asymptotic depth of invariant chains of edge ideals
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917772272861184 |
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| author | Hoa, Tran Quang Hoang, Do Trong Van Le, Dinh Nguyen, Hop D. Nguyen, Thai Thanh |
| author_facet | Hoa, Tran Quang Hoang, Do Trong Van Le, Dinh Nguyen, Hop D. Nguyen, Thai Thanh |
| contents | We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic depth of invariant chains of edge ideals Hoa, Tran Quang Hoang, Do Trong Van Le, Dinh Nguyen, Hop D. Nguyen, Thai Thanh Commutative Algebra Combinatorics 13A50, 13C15, 13D02, 13F20, 16P70, 16W22 We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes. |
| title | Asymptotic depth of invariant chains of edge ideals |
| topic | Commutative Algebra Combinatorics 13A50, 13C15, 13D02, 13F20, 16P70, 16W22 |
| url | https://arxiv.org/abs/2409.06252 |