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