East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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COMMUTATIVITY OF ASSOCIATION SCHEMES OF ORDER pq

  • Hanaki, Akihide (Department of Mathematical Sciences, Faculty of Science, Shinshu University) ;
  • Hirasaka, Mitsugu (Department of Mathematics, Pusan National University)
  • Received : 2012.11.08
  • Accepted : 2013.01.11
  • Published : 2013.01.31
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Abstract

Let (X, S) be an association scheme where X is a finite set and S is a partition of $X{\times}X$. The size of X is called the order of (X, S). We define $\mathcal{C}$ 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 $\mathcal{C}$ and it is conjectured that each prime square is belonged to $\mathcal{C}$. 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 for the conjecture in case where $p=q$.

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References

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