Show simple item record

Files in this item

Thumbnail

Item metadata

dc.contributor.authorCameron, Peter J.
dc.contributor.authorEberhard, Sean
dc.date.accessioned2019-10-29T09:30:04Z
dc.date.available2019-10-29T09:30:04Z
dc.date.issued2019-10-27
dc.identifier.citationCameron , P J & Eberhard , S 2019 , ' Association schemes for diagonal groups ' , Australasian Journal of Combinatorics , vol. 75 , no. 3 , pp. 357-364 . < https://ajc.maths.uq.edu.au/pdf/75/ajc_v75_p357.pdf >en
dc.identifier.issn2202-3518
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.identifier.urihttp://hdl.handle.net/10023/18797
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.language.isoeng
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.subjectMathematics(all)en
dc.subjectT-NDASen
dc.subject.lccQAen
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
dc.identifier.urlhttps://ajc.maths.uq.edu.au/pdf/78/ajc_v78_p450.pdfen
dc.identifier.urlhttps://ajc.maths.uq.edu.au/pdf/75/ajc_v75_p357.pdfen


This item appears in the following Collection(s)

Show simple item record