M. Hirasaka

activity

20102021

most citedUpper bounds on cyclotomic numbers

8 citations · 13 across the 11 of their papers we have counts for

collaborators

16 papers

math.CO2021

Association schemes with a certain type of $p$ -subschemes

Wasim Abbas, Mitsugu Hirasaka

In this article, we focus on association schemes with some properties derived from the orbitals of a transitive permutation group $G$ with a one-point stabilizer $H$ satisfying $H…

math.CO2018

Two-valenced association schemes and the Desargues theorem

Mitsugu Hirasaka, Kijung Kim, Ilia Ponomarenko

The main goal of the paper is to establish a sufficient condition for a two-valenced association scheme to be schurian and separable. To this end, an analog of the Desargues theore…

math.CO2018★ 2 cited

Characterization of finite metric space by their isometric sequences

Mitsugu Hirasaka, Masashi Shinohara

Let $(X, d)$ be a finite metric space with $∣ X ∣ = n$ . For a positive integer $k$ we define $A_{k} (X)$ to be the quotient set of all $k$ -subsets of $X$ by isometry, and we denote $|A_k(X…

math.CO2018

Characterization of finite colored spaces with certain conditions

Mitsugu Hirasaka, Masashi Shinohara

A colored space is the pair $(X, r)$ of a set $X$ and a function $r$ whose domain is $(2 X)$ . Let $(X, r)$ be a finite colored space and $Y, Z \subseteq X$ . We shall write $Y\si…

math.CO2018

Schurity and separability of quasiregular coherent configurations

Mitsugu Hirasaka, Kijung Kim, Ilia Ponomarenko

A permutation group is said to be quasiregular if every its transitive constituent is regular, and a quasiregular coherent configuration can be thought as a combinatorial analog of…

math.CO2017

New families of Hadamard matrices with maximum excess

Mitsugu Hirasaka, Koji Momihara, Sho Suda

In this paper, we find regular or biregular Hadamard matrices with maximum excess by negating some rows and columns of known Hadamard matrices obtained from quadratic residues of f…

math.CO2016

The number of ideals of $Z [x]$ containing $x (x - α) (x - β)$ with given index

Mitsugu Hirasaka, Semin Oh

It is well-known that a connected regular graph is strongly-regular if and only if its adjacency matrix has exactly three eigenvalues. Let $B$ denote an integral square matrix and…

math.CO2016

Association schemes all of whose symmetric fusion schemes are integral

Mitsugu Hirasaka, Kijung Kim, Semin Oh

In this paper we aim to characterize association schemes all of whose symmetric fusion schemes have only integral eigenvalues, and classify those obtained from a regular action of…

math.RA2015★ 2 cited

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

Allen Herman, Mitsugu Hirasaka, Semin Oh

The zeta function of an integral lattice $Λ$ is the generating function $ζ_{Λ} (s) = n = 0 \sum \infty a_{n} n^{- s}$ , whose coefficients count the number of left ideals of $Λ$ …

math.CO2015★ 1 cited

Association schemes in which the thin residue is an elementary abelian $p$ -group of rank $2$

Mitsugu Hirasaka, Kijung Kim

In this article, we investigate the existence and schurity problem of association schemes whose thin residues are isomorphic to an elementary abelian $p$ -group of rank $2$ .

math.CO2014

Isomorphism classes of association schemes induced by Hadamard matrices

Mitsugu Hirasaka, Kijung Kim, Hyonju Yu

Every Hadamard matrix $H$ of order $n > 1$ induces a graph with $4 n$ vertices, called the Hadamard graph $Γ (H)$ of $H$ . Since $Γ (H)$ is a distance-regular graph with diameter $4$ ,…

math.CO2014

Uniqueness of Butson Hadamard matrices of small degrees

Kyoung-Tark Kim, Hirasaka Mitsugu, Yoshihiro Mizoguchi

For positive integers $m$ and $n$ , we denote by $BH (m, n)$ the set of all $H \in M_{n \times n} (C)$ such that $H H^{*} = n I_{n}$ and each entry of $H$ is an $m$ -th root…

math.CO2013

Coherent configurations over copies of association schemes of prime order

Reza Sharafdini, Mitsugu Hirasaka

Let $G$ be a group acting faithfully and transitively on $Ω_{i}$ for $i = 1, 2$ . A famous theorem by Burnside implies the following fact: If $∣ Ω_{1} ∣ = ∣ Ω_{2} ∣$ is a prime and the rank of one…

math.CO2012

On $p$ -schemes of order $p^{3}$

Jung Rae Cho, Mitsugu Hirasaka, Kijung Kim

Let $(X, S)$ be a $p$ -scheme of order $p^{3}$ and $T$ the thin residue of $S$ . Now we assume that $T$ has valency $p^{2}$ . It is easy to see that one of the following holds: (i) $|T|=p^…

math.CO2011★ 8 cited

Upper bounds on cyclotomic numbers

Koichi Betsumiya, Mitsugu Hirasaka, Takao Komatsu +1

In this article, we give upper bounds for cyclotomic numbers of order e over a finite field with q elements, where e is a divisor of q-1. In particular, we show that under certain…

math.CO2010

Characterization of Balanced Coherent Configurations

Mitsugu Hirasaka, Reza Sharafdini

Let $G$ be a group acting on a finite set $Ω$ . Then $G$ acts on $Ω \times Ω$ by its entry-wise action and its orbits form the basis relations of a coherent configuration (or shortly…

Association schemes with a certain type of p-subschemes

Two-valenced association schemes and the Desargues theorem

Characterization of finite metric space by their isometric sequences

Characterization of finite colored spaces with certain conditions

Schurity and separability of quasiregular coherent configurations

New families of Hadamard matrices with maximum excess

The number of ideals of Z[x] containing x(x−α)(x−β) with given index

Association schemes all of whose symmetric fusion schemes are integral

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

Association schemes in which the thin residue is an elementary abelian p-group of rank 2

Isomorphism classes of association schemes induced by Hadamard matrices

Uniqueness of Butson Hadamard matrices of small degrees

Coherent configurations over copies of association schemes of prime order

On p-schemes of order p3

Upper bounds on cyclotomic numbers

Characterization of Balanced Coherent Configurations

Association schemes with a certain type of $p$ -subschemes

The number of ideals of $Z [x]$ containing $x (x - α) (x - β)$ with given index

Association schemes in which the thin residue is an elementary abelian $p$ -group of rank $2$

On $p$ -schemes of order $p^{3}$