A characterization of exceptional pseudocyclic association schemes by multidimensional intersection numbers

Gang Chen, Jiawei He, Ilia Ponomarenko, Andrey Vasil'ev

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, groups, coherent configurations

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DOI: https://doi.org/10.26493/1855-3974.2405.b43

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications