On the association scheme of perfect matchings and their designs
Abstract
We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph K 2 n . We show that they are special subsets of the association scheme obtained from the Gelfand pair ( S 2 n , S 2 ≀ 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 2 n ] and using the representation theory of S 2 n .
Fields of Study & Subjects
Finite Group Theory Research
graph theory and CDMA systems
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Algebraic Combinatorics
- Volume
- 9
- Issue
- 3
- Pages
- 789–809
- Publication date
- 1 July 2026
- Language
- EN