Critical groups of arithmetical structures on star graphs and complete graphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911882693050368 |
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| author | Archer, Kassie Diaz-Lopez, Alexander Glass, Darren Louwsma, Joel |
| author_facet | Archer, Kassie Diaz-Lopez, Alexander Glass, Darren Louwsma, Joel |
| contents | An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of these is a finite abelian group known as its critical group. We show how to determine the critical group of an arithmetical structure on a star graph or complete graph in terms of the entries of the arithmetical structure. We use this to investigate which finite abelian groups can occur as critical groups of arithmetical structures on these graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02114 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Critical groups of arithmetical structures on star graphs and complete graphs Archer, Kassie Diaz-Lopez, Alexander Glass, Darren Louwsma, Joel Combinatorics Number Theory 05C50 (Primary) 05C25, 11C20, 11D68 (Secondary) An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of these is a finite abelian group known as its critical group. We show how to determine the critical group of an arithmetical structure on a star graph or complete graph in terms of the entries of the arithmetical structure. We use this to investigate which finite abelian groups can occur as critical groups of arithmetical structures on these graphs. |
| title | Critical groups of arithmetical structures on star graphs and complete graphs |
| topic | Combinatorics Number Theory 05C50 (Primary) 05C25, 11C20, 11D68 (Secondary) |
| url | https://arxiv.org/abs/2301.02114 |