A characterization of exceptional pseudocyclic association schemes by multidimensional intersection numbers

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A characterization of exceptional pseudocyclic association schemes by multidimensional intersection numbers. / Chen, Gang; He, Jiawei; Ponomarenko, Ilia et al.

In: Ars Mathematica Contemporanea, Vol. 21, No. 1, #P1.10, 2021.

Research output: Contribution to journal › Article › peer-review

Author

Chen, Gang ; He, Jiawei ; Ponomarenko, Ilia et al. / A characterization of exceptional pseudocyclic association schemes by multidimensional intersection numbers. In: Ars Mathematica Contemporanea. 2021 ; Vol. 21, No. 1.

BibTeX

@article{6f62b3ac5ba140c1a620b8dc08a88c9d,

title = "A characterization of exceptional pseudocyclic association schemes by multidimensional intersection numbers",

abstract = "Recent classification of 3/2 -transitive permutation groups leaves us with three infinite families of groups which are neither 2-transitive, nor Frobenius, nor one-dimensional affine. The groups of the first two families correspond to special actions of PSL(2, q) and PΓL(2, q), whereas those of the third family are the affine solvable subgroups of AGL(2, q) found by D. Passman in 1967. The association schemes of the groups in each of these families are known to be pseudocyclic. It is proved that apart from three particular cases, each of these exceptional pseudocyclic schemes is characterized up to isomorphism by the tensor of its 3-dimensional intersection numbers.",

keywords = "Association schemes, Coherent configurations, Groups",

author = "Gang Chen and Jiawei He and Ilia Ponomarenko and Andrey Vasil'Ev",

note = "Funding Information: *The author was supported by the NSFC grant No. 11971189. †The author was supported by the NSFC grant No. 11971189. ‡Corresponding author. The author was supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. §The author was supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. E-mail addresses: chengangmath@mail.ccnu.edu.cn (Gang Chen), hjwywh@mails.ccnu.edu.cn (Jiawei He), inp@pdmi.ras.ru (Ilia Ponomarenko), vasand@math.nsc.ru (Andrey Vasil{\textquoteright}ev) Publisher Copyright: {\textcopyright} 2021 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.",

year = "2021",

doi = "10.26493/1855-3974.2405.b43",

language = "English",

volume = "21",

journal = "Ars Mathematica Contemporanea",

issn = "1855-3966",

publisher = "DMFA Slovenije",

number = "1",

}

RIS

TY - JOUR

T1 - A characterization of exceptional pseudocyclic association schemes by multidimensional intersection numbers

AU - Chen, Gang

AU - He, Jiawei

AU - Ponomarenko, Ilia

AU - Vasil'Ev, Andrey

N1 - Funding Information: *The author was supported by the NSFC grant No. 11971189. †The author was supported by the NSFC grant No. 11971189. ‡Corresponding author. The author was supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. §The author was supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. E-mail addresses: chengangmath@mail.ccnu.edu.cn (Gang Chen), hjwywh@mails.ccnu.edu.cn (Jiawei He), inp@pdmi.ras.ru (Ilia Ponomarenko), vasand@math.nsc.ru (Andrey Vasil’ev) Publisher Copyright: © 2021 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.

PY - 2021

Y1 - 2021

N2 - Recent classification of 3/2 -transitive permutation groups leaves us with three infinite families of groups which are neither 2-transitive, nor Frobenius, nor one-dimensional affine. The groups of the first two families correspond to special actions of PSL(2, q) and PΓL(2, q), whereas those of the third family are the affine solvable subgroups of AGL(2, q) found by D. Passman in 1967. The association schemes of the groups in each of these families are known to be pseudocyclic. It is proved that apart from three particular cases, each of these exceptional pseudocyclic schemes is characterized up to isomorphism by the tensor of its 3-dimensional intersection numbers.

AB - Recent classification of 3/2 -transitive permutation groups leaves us with three infinite families of groups which are neither 2-transitive, nor Frobenius, nor one-dimensional affine. The groups of the first two families correspond to special actions of PSL(2, q) and PΓL(2, q), whereas those of the third family are the affine solvable subgroups of AGL(2, q) found by D. Passman in 1967. The association schemes of the groups in each of these families are known to be pseudocyclic. It is proved that apart from three particular cases, each of these exceptional pseudocyclic schemes is characterized up to isomorphism by the tensor of its 3-dimensional intersection numbers.

KW - Association schemes

KW - Coherent configurations

KW - Groups

UR - http://www.scopus.com/inward/record.url?scp=85118098053&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.2405.b43

DO - 10.26493/1855-3974.2405.b43

M3 - Article

AN - SCOPUS:85118098053

VL - 21

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3966

IS - 1

M1 - #P1.10

ER -

ID: 34569830