On the association scheme of perfect matchings and their designs
L.-A.D. Klawuhn, J. Bamberg, Algebraic Combinatorics 9 (2026) 789–809.
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Klawuhn, Lukas-André DominikLibreCat 
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Bamberg, John
;
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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Journal Title
Algebraic Combinatorics
Volume
9
Issue
3
Page
789-809
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Klawuhn L-AD, Bamberg J. On the association scheme of perfect matchings and their designs. Algebraic Combinatorics. 2026;9(3):789-809. doi:10.5802/alco.490
Klawuhn, L.-A. D., & Bamberg, J. (2026). On the association scheme of perfect matchings and their designs. Algebraic Combinatorics, 9(3), 789–809. https://doi.org/10.5802/alco.490
@article{Klawuhn_Bamberg_2026, title={On the association scheme of perfect matchings and their designs}, volume={9}, DOI={10.5802/alco.490}, number={3}, journal={Algebraic Combinatorics}, author={Klawuhn, Lukas-André Dominik and Bamberg, John}, year={2026}, pages={789–809} }
Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs.” Algebraic Combinatorics 9, no. 3 (2026): 789–809. https://doi.org/10.5802/alco.490.
L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings and their designs,” Algebraic Combinatorics, vol. 9, no. 3, pp. 789–809, 2026, doi: 10.5802/alco.490.
Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs.” Algebraic Combinatorics, vol. 9, no. 3, 2026, pp. 789–809, doi:10.5802/alco.490.
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