3 citations · 8 across the 12 of their papers we have counts for
13 papers
Multivariate - and -polynomial structures of generalized Johnson association schemes
Hirotake Kurihara
Let be a commutative association scheme of class on . We construct the generalized Johnson association scheme on partial maps…
Twisted primitive group association schemes
Akihiro Higashitani, Masanari Kamiya, Hirotake Kurihara
We give results on the question of whether the intersection numbers of a primitive group association scheme determine it up to combinatorial isomorphism. For $G=\operatorname{PSL}(…
Imprimitive association schemes and elimination theory
Akihiro Higashitani, Hirotake Kurihara
We prove that a commutative association scheme is imprimitive if and only if it admits a multivariate - or -polynomial structure with respect to an elimination-type monomial…
Classification of generalized Alexander quandles
Akihiro Higashitani, Seiichi Kamada, Jin Kosaka +1
The aim of this paper is to provide a new characterization of isomorphism classes of generalized Alexander quandles in terms of the underlying groups and their automorphisms. This…
Multivariate P- and/or Q-polynomial association schemes
Eiichi Bannai, Hirotake Kurihara, Da Zhao +1
The classification problem of - and -polynomial association schemes has been one of the central problems in algebraic combinatorics. Generalizing the concept of - and -…
Generalized Alexander quandles of finite groups and their characterizations
Akihiro Higashitani, Hirotake Kurihara
The goal of this paper is to characterization generalized Alexander quandles of finite groups in the language of the underlying groups. Firstly, we prove that if finite groups …
The least Euclidean distortion constant of a distance-regular graph
Sebastian M. Cioabă, Himanshu Gupta, Ferdinand Ihringer +1
In 2008, Vallentin made a conjecture involving the least distortion of an embedding of a distance-regular graph into Euclidean space. Vallentin's conjecture implies that for a leas…
Homogeneous quandles arising from automorphisms of symmetric groups
Akihiro Higashitani, Hirotake Kurihara
Quandle is an algebraic system with one binary operation, but it is quite different from a group. Quandle has its origin in the knot theory and good relationships with the theory o…
Great antipodal sets of complex Grassmannian manifolds as designs with the smallest cardinalities
Hirotake Kurihara, Takayuki Okuda
The aim of this paper is a characterization of great antipodal sets of complex Grassmannian manifolds as certain designs with the smallest cardinalities.
An excess theorem for spherical 2-designs
Hirotake Kurihara
We give an excess theorem for spherical 2-designs. This theorem is a dual version of the spectral excess theorem for graphs, which gives a characterization of distance-regular grap…
A spectral equivalent condition of the -polynomial property for association schemes
Hirotake Kurihara, Hiroshi Nozaki
We give an equivalent condition of the -polynomial property of symmetric association schemes.
Character tables of association schemes based on attenuated spaces
Hirotake Kurihara
The set of subspaces of a given dimension in an attenuated space has a structure of a symmetric association scheme and this association scheme is called an association scheme based…
A characterization of Q-polynomial association schemes
Hirotake Kurihara, Hiroshi Nozaki
We prove a necessary and sufficient condition for a symmetric association scheme to be a Q-polynomial scheme.