On the association scheme of perfect matchings and their designs
L.-A.D. Klawuhn, J. Bamberg, (2025).
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Klawuhn, Lukas-André DominikLibreCat 
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Bamberg, John
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Bamberg, JohnDepartment
Abstract
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 $S_{2n}$.
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Klawuhn L-AD, Bamberg J. On the association scheme of perfect matchings and their designs. Published online 2025.
Klawuhn, L.-A. D., & Bamberg, J. (2025). On the association scheme of perfect matchings and their designs.
@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} }
Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs,” 2025.
L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings and their designs.” 2025.
Klawuhn, Lukas-André Dominik, and John Bamberg. On the Association Scheme of Perfect Matchings and Their Designs. 2025.
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