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COMMUTATIVITY OF ASSOCIATION SCHEMES OF ORDER pq

Akihide Hanaki, Mitsugu Hirasaka
2013 East Asian Mathematical Journal  
Let (X, S) be an association scheme where X is a finite set and S is a partition of X × X. The size of X is called the order of (X, S). We define C to be the set of positive integers m such that each association scheme of order m is commutative. It is known that each prime is belonged to C and it is conjectured that each prime square is belonged to C. In this article we give a sufficient condition for a scheme of order pq to be commutative where p and q are primes, and obtain a partial answer
more » ... a partial answer for the conjecture in case where p = q.
doi:10.7858/eamj.2013.004 fatcat:ae3xwr5r6rad5bqw4wncigy3we