On the association scheme of perfect matchings and their designs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912971606720512 |
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| author | Bamberg, John Klawuhn, Lukas |
| author_facet | Bamberg, John Klawuhn, Lukas |
| contents | We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph $K_{2n}$. We show that they are special subsets of the association scheme obtained from the Gelfand pair $(S_{2n},S_2 \wr S_n)$. This unifies and extends results by Cameron (1976) and gives rise to new existence and non-existence results. Our methods involve working in the group algebra $\mathbb{C}[S_{2n}]$ and using the representation theory of $S_{2n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the association scheme of perfect matchings and their designs Bamberg, John Klawuhn, Lukas Combinatorics We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph $K_{2n}$. We show that they are special subsets of the association scheme obtained from the Gelfand pair $(S_{2n},S_2 \wr S_n)$. This unifies and extends results by Cameron (1976) and gives rise to new existence and non-existence results. Our methods involve working in the group algebra $\mathbb{C}[S_{2n}]$ and using the representation theory of $S_{2n}$. |
| title | On the association scheme of perfect matchings and their designs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.00813 |