Mitsugu Hirasaka

Sufficient conditions for a scheme to originate from a group

We present two different sufficient conditions for a scheme to originate from a transitive permutation group.

Construction of association schemes from difference sets

Let H and F be two finite groups. In group theory it is known that an extension G of H by F is characterized by the action of F on H and a factor set associated with the action, and the two-dimensional cohomology group with respect to the action is defined when H is Abelian. In this paper we consider an analogy of the above for association schemes and construct such extensions of association schemes from a difference set when H is an elementary Abelian group.

Characterization of association schemes by equitable partitions

In this paper we deal with equitable partitions of association schemes. We try to generalize a result in group theory and show examples that a generalization of a certain property conjectured for permutation groups does not hold for association schemes.

Uniqueness of Butson Hadamard matrices of small degrees

Let BH n × n ( m ) be the set of n × n Butson Hadamard matrices where all the entries are m-th roots of unity. For H 1 , H 2 ? BH n × n ( m ) , we say that H 1 is equivalent to H 2 if H 1 = P H 2 Q for some monomial matrices P and Q whose nonzero entries are m-th roots of unity. In the present paper we show by computer search that all the matrices in BH 17 × 17 ( 17 ) are equivalent to the Fourier matrix of degree 17. Furthermore we shall prove that, for a prime number p, a matrix in BH p × p ( p ) which is not equivalent to the Fourier matrix of degree p gives rise to a non-Desarguesian projective plane of order p.

On p-covalenced association schemes

Let (X,S) denote an association scheme where X is a finite set. For a prime p we say that (X,S) is p-covalenced (p-valenced) if every multiplicity (valency, respectively) of (X,S) is a power of p. In the character theory of finite groups Itos theorem states that a finite group G has a normal abelian p-complement if and only if every character degree of G is a power of p. In this article we generalize Itos theorem to p-valenced association schemes, i.e., a p-valenced association scheme (X,S) has a normal p-covalenced p-complement if and only if (X,S) is p-covalenced.

Coherent configurations over copies of association schemes of prime order

Let

On imprimitive multiplicity-free permutation groups the degree of which is the product of two distinct primes

G

Equitable Partitions of Flat Association Schemes

be a group acting faithfully and transitively on

Zeta functions for tensor products of locally coprime integral adjacency algebras of association schemes

\Omega_i

Isomorphism classes of association schemes induced by Hadamard matrices

for