Self‐dual association schemes, fusions of Hamming schemes, and partial geometric designs
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Combinatorial Designs"
DOI: 10.1002/jcd.21889
Abstract: Partial geometric designs can be constructed from basic relations of association schemes. An infinite family of partial geometric designs were constructed from the fusion schemes of certain Hamming schemes in work by Nowak et al.… read more here.
Keywords: dual association; geometric designs; partial geometric; self dual ... See more keywords
Design Theory from the Viewpoint of Algebraic Combinatorics
Sign Up to like & getrecommendations! Published in 2017 at "Graphs and Combinatorics"
DOI: 10.1007/s00373-016-1739-2
Abstract: We give a survey on various design theories from the viewpoint of algebraic combinatorics. We will start with the following themes.(i)The similarity between spherical t-designs and combinatorial t-designs, as well as t-designs in Q-polynomial association… read more here.
Keywords: algebraic combinatorics; association schemes; viewpoint algebraic; relative designs ... See more keywords
Spherical Embeddings of Symmetric Association Schemes in 3-Dimensional Euclidean Space
Sign Up to like & getrecommendations! Published in 2020 at "Graphs and Combinatorics"
DOI: 10.1007/s00373-019-02075-6
Abstract: We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with $$m_1 = 3$$ m 1 = 3 . read more here.
Keywords: symmetric association; euclidean space; dimensional euclidean; association ... See more keywords
On Tight 4-Designs in Hamming Association Schemes
Sign Up to like & getrecommendations! Published in 2020 at "Combinatorica"
DOI: 10.1007/s00493-019-4115-z
Abstract: We complete the classification of tight 4-designs in Hamming association schemes H ( n , q ), i.e., that of tight orthogonal arrays of strength 4, which had been open since a result by Noda… read more here.
Keywords: tight designs; schemes tight; association schemes; association ... See more keywords
Association Schemes with at Most Two Nonlinear Irreducible Characters and Applications to Finite Groups
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-018-7072-3
Abstract: An irreducible character χ of an association scheme is called nonlinear if the multiplicity of χ is greater than 1. The main result of this paper gives a characterization of commutative association schemes with at… read more here.
Keywords: two nonlinear; association schemes; nonlinear irreducible; schemes two ... See more keywords
Indecomposable decompositions of modular standard modules for two families of association schemes
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Algebraic Combinatorics"
DOI: 10.1007/s10801-017-0758-2
Abstract: We investigate the indecomposable decomposition of the modular standard modules of two families of association schemes of finite order. First, we show that, for each prime number p, the standard module over a field F… read more here.
Keywords: modules two; association schemes; modular standard; two families ... See more keywords
Schur rings and association schemes whose thin residues are thin
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2017.07.015
Abstract: Abstract The thin residue is an important concept in the theory of association schemes. Association schemes whose thin residues are thin have been studied in several papers. In this paper we construct a new class… read more here.
Keywords: association schemes; residues thin; whose thin; association ... See more keywords
On the association schemes with the thin radical series
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Algebra and Its Applications"
DOI: 10.1142/s0219498819500713
Abstract: In this paper, we first show that the wedge product of a thin association scheme and a schurian association scheme is schurian. Then as an application of this result, we investigate the schurity problem for… read more here.
Keywords: thin radical; schemes thin; association; association schemes ... See more keywords