On the association scheme of perfect matchings and their designs
Abstract
We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph K2n. We show that they are special subsets of the association scheme obtained from the Gelfand pair (S2n,S2 Sn). 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[S2n] and using the representation theory of S2n.
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