[{"date_created":"2025-07-02T07:37:23Z","status":"public","year":"2025","type":"preprint","language":[{"iso":"eng"}],"_id":"60491","date_updated":"2025-07-02T07:47:09Z","author":[{"first_name":"Lukas-André Dominik","full_name":"Klawuhn, Lukas-André Dominik","last_name":"Klawuhn","id":"91965","orcid":"0009-0009-7736-4885"},{"last_name":"Bamberg","first_name":"John","full_name":"Bamberg, John"}],"title":"On the association scheme of perfect matchings and their designs","abstract":[{"lang":"eng","text":"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 $S_{2n}$."}],"user_id":"91965","citation":{"bibtex":"@article{Klawuhn_Bamberg_2025, title={On the association scheme of perfect matchings and their designs}, author={Klawuhn, Lukas-André Dominik and Bamberg, John}, year={2025} }","mla":"Klawuhn, Lukas-André Dominik, and John Bamberg. <i>On the Association Scheme of Perfect Matchings and Their Designs</i>. 2025.","short":"L.-A.D. Klawuhn, J. Bamberg, (2025).","ama":"Klawuhn L-AD, Bamberg J. On the association scheme of perfect matchings and their designs. Published online 2025.","apa":"Klawuhn, L.-A. D., &#38; Bamberg, J. (2025). <i>On the association scheme of perfect matchings and their designs</i>.","ieee":"L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings and their designs.” 2025.","chicago":"Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs,” 2025."},"external_id":{"arxiv":["2507.00813"]},"department":[{"_id":"100"}]}]