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dc.contributor.authorAljohani, Mohammed
dc.contributor.authorBamberg, John
dc.contributor.authorCameron, Peter Jephson
dc.identifier.citationAljohani , M , Bamberg , J & Cameron , P J 2018 , ' Synchronization and separation in the Johnson schemes ' , Portugaliae Mathematica , vol. 74 , no. 3 , pp. 213-232 .
dc.identifier.otherPURE: 250847949
dc.identifier.otherPURE UUID: 142298fa-e33f-469c-94b9-c350fb322180
dc.identifier.otherScopus: 85041713788
dc.identifier.otherORCID: /0000-0003-3130-9505/work/58055721
dc.identifier.otherWOS: 000427321500004
dc.description.abstractRecently Peter Keevash solved asymptotically the existence question for Steiner systems by showing that S(t,k,n) exists whenever the necessary divisibility conditions on the parameters are satisfied and n is sufficiently large in terms of k and t. The purpose of this paper is to make a conjecture which if true would be a significant extension of Keevash's theorem, and to give some theoretical and computational evidence for the conjecture. We phrase the conjecture in terms of the notions (which we define here) of synchronization and separation for association schemes. These definitions are based on those for permutation groups which grow out of the theory of synchronization in finite automata. In this theory, two classes of permutation groups (called synchronizing and separating) lying between primitive and 2-homogeneous are defined. A big open question is how the permutation group induced by Sn on k-subsets of {1,...,n} fits in this hierarchy; our conjecture would give a solution to this problem for n large in terms of k.
dc.relation.ispartofPortugaliae Mathematicaen
dc.rightsCopyright © 2017, European Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectSteiner systemsen
dc.subjectQA Mathematicsen
dc.titleSynchronization and separation in the Johnson schemesen
dc.typeJournal articleen
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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