Ask zeta functions of joins of graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918021614796800 |
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| author | Rossmann, Tobias Voll, Christopher |
| author_facet | Rossmann, Tobias Voll, Christopher |
| contents | In previous work (arXiv:1908.09589), we studied rational generating functions ("ask zeta functions") associated with graphs and hypergraphs. These functions encode average sizes of kernels of generic matrices with support constraints determined by the graph or hypergraph in question, with applications to the enumeration of linear orbits and conjugacy classes of unipotent groups. In the present article, we turn to the effect of a natural graph-theoretic operation on associated ask zeta functions. Specifically, we show that two instances of rational functions, $W^-_Γ(X,T)$ and $W^\sharp_Γ(X,T)$, associated with a graph $Γ$ are both well-behaved under taking joins of graphs. In the former case, this has applications to zeta functions enumerating conjugacy classes associated with so-called graphical groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ask zeta functions of joins of graphs Rossmann, Tobias Voll, Christopher Combinatorics Group Theory 11M41, 05C50, 15B33, 05A15, 11S80, 20D15, 20E45 In previous work (arXiv:1908.09589), we studied rational generating functions ("ask zeta functions") associated with graphs and hypergraphs. These functions encode average sizes of kernels of generic matrices with support constraints determined by the graph or hypergraph in question, with applications to the enumeration of linear orbits and conjugacy classes of unipotent groups. In the present article, we turn to the effect of a natural graph-theoretic operation on associated ask zeta functions. Specifically, we show that two instances of rational functions, $W^-_Γ(X,T)$ and $W^\sharp_Γ(X,T)$, associated with a graph $Γ$ are both well-behaved under taking joins of graphs. In the former case, this has applications to zeta functions enumerating conjugacy classes associated with so-called graphical groups. |
| title | Ask zeta functions of joins of graphs |
| topic | Combinatorics Group Theory 11M41, 05C50, 15B33, 05A15, 11S80, 20D15, 20E45 |
| url | https://arxiv.org/abs/2505.10263 |