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dc.contributor.authorCameron, Peter J.
dc.contributor.authorEberhard, Sean
dc.identifier.citationCameron , P J & Eberhard , S 2019 , ' Association schemes for diagonal groups ' , Australasian Journal of Combinatorics , vol. 75 , no. 3 , pp. 357-364 . < >en
dc.identifier.otherPURE: 262388178
dc.identifier.otherPURE UUID: e033e6fb-c8a6-4f45-a414-475450bb4406
dc.identifier.otherORCID: /0000-0003-3130-9505/work/64034525
dc.identifier.otherScopus: 85074331084
dc.identifier.otherWOS: 000500323000006
dc.description.abstractFor any finite group G, and any positive integer n, we construct an association scheme which admits the diagonal group Dn(G) as a group of automorphisms. The rank of the association scheme is the number of partitions of n into at most |G| parts, so is p(n) if |G| ≥ n; its parameters depend only on n and |G|. For n=2, the association scheme is trivial, while for n=3 its relations are the Latin square graph associated with the Cayley table of G and its complement. A transitive permutation group G is said to be AS-free if there is no non-trivial association scheme admitting G as a group of automorphisms. A consequence of our construction is that an AS-free group must be either 2-homogeneous or almost simple. We construct another association scheme, finer than the above scheme if n>3, from the Latin hypercube consisting of n-tuples of elements of G with product the identity.
dc.relation.ispartofAustralasian Journal of Combinatoricsen
dc.rightsCopyright © The author(s). Released under the CC BY 4.0 International License.en
dc.subjectAssociation schemeen
dc.subjectDiagonal groupen
dc.subjectLatin squareen
dc.subjectQA Mathematicsen
dc.titleAssociation schemes for diagonal groupsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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