COMMUTATIVITY OF ASSOCIATION SCHEMES OF ORDER pq
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Let (X; S) be an association scheme where X is a nite set and S is a partition of X X. The size of X is called the order of (X; S). We de ne 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 su cient condition for a scheme of order pq to be commutative where p and q are primes, and obtain a partial answer for the conjecture in case where p = q.
Abstract
Let (X; S) be an association scheme where X is a nite set and S is a partition of X X. The size of X is called the order of (X; S). We de ne 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 su cient condition for a scheme of order pq to be commutative where p and q are primes, and obtain a partial answer for the conjecture in case where p = q.
참고문헌 (14)
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