On the association scheme of perfect matchings and their designs

2025/07/01 by Bamberg, John, Klawuhn, Lukas
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.00813

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,S₂ \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 ℂ[S_2n] and using the representation theory of S_2n.

Citations

• Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry
• Intersecting Families of Perfect Matchings

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• Erdős-Ko-Rado for Perfect Matchings
• Extended double covers of non-symmetric association schemes of class 2
• Properties of Commutative Association Schemes derived by FGLM Techniques
• On the second largest eigenvalue of certain graphs in the perfect matching association scheme
• Hypergraph matchings and designs