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Terwilliger algebras of direct and wreath products of association schemes
Hanaki, Akihide,Kim, Kijung,Maekawa, Yu Elsevier 2011 Journal of algebra Vol.343 No.1
<P><B>Abstract</B></P><P>We will consider structures of Terwilliger algebras of direct and wreath products of association schemes. In general, it is difficult to determine the structure of the Terwilliger algebras though they are known to be semisimple C-algebras. But, we get the structure of Terwilliger algebras of these cases under some assumptions.</P>
COMMUTATIVITY OF ASSOCIATION SCHEMES OF ORDER pq
Hanaki, Akihide,Hirasaka, Mitsugu The Youngnam Mathematical Society 2013 East Asian mathematical journal Vol.29 No.1
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 $p=q$.
COMMUTATIVITY OF ASSOCIATION SCHEMES OF ORDER pq
Akihide Hanaki,히라사카 영남수학회 2013 East Asian mathematical journal Vol.29 No.1
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.