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Families of association schemes on triples from two-transitive groupsJose Maria P. Balmaceda,
Dom Vito A. Briones, 2025, original scientific article
Abstract: Association schemes on triples (ASTs) are ternary analogues of classical association schemes. Similar to how Schurian association schemes arise from transitive groups, ASTs arise from two-transitive groups. In this paper, we obtain the third valencies and the number of relations of the ASTs obtained from two-transitive permutation groups. Further, we obtain the intersection numbers of the ASTs produced by PΓL(k, n), PSL(2, n), AΓL(k, n), and the sporadic two-transitive groups. In particular, the ASTs from the actions of PΓL(k, n), PSL(2, n), and the sporadic groups are commutative.
Keywords: association scheme on triples, permutation group, ternary algebra, algebraic combinatorics
Published in RUP: 21.10.2025; Views: 801; Downloads: 10
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