Artin-Ihara L-functions for hypergraphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916253210247168 |
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| author | Eyler, Mason Jun, Jaiung |
| author_facet | Eyler, Mason Jun, Jaiung |
| contents | We generalize Artin-Ihara L-functions for graphs to hypergraphs by exploring several analogous notions, such as (unramified) Galois coverings and Frobenius elements. To a hypergraph $H$, one can naturally associate a bipartite graph $B_H$ encoding incidence relations of $H$. We study Artin-Ihara $L$-functions of hypergraphs $H$ by using Artin-Ihara $L$-functions of associated bipartite graphs $B_H$. As a result, we prove various properties for Artin-Ihara L-functions for hypergraphs. For instance, we prove that the Ihara zeta function of a hypergraph $H$ can be written as a product of Artin-Ihara $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15873 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Artin-Ihara L-functions for hypergraphs Eyler, Mason Jun, Jaiung Combinatorics 05C38(primary), 05C65 (secondary) We generalize Artin-Ihara L-functions for graphs to hypergraphs by exploring several analogous notions, such as (unramified) Galois coverings and Frobenius elements. To a hypergraph $H$, one can naturally associate a bipartite graph $B_H$ encoding incidence relations of $H$. We study Artin-Ihara $L$-functions of hypergraphs $H$ by using Artin-Ihara $L$-functions of associated bipartite graphs $B_H$. As a result, we prove various properties for Artin-Ihara L-functions for hypergraphs. For instance, we prove that the Ihara zeta function of a hypergraph $H$ can be written as a product of Artin-Ihara $L$-functions. |
| title | Artin-Ihara L-functions for hypergraphs |
| topic | Combinatorics 05C38(primary), 05C65 (secondary) |
| url | https://arxiv.org/abs/2309.15873 |