Please use this identifier to cite or link to this item: http://archive.cmb.ac.lk:8080/xmlui/handle/70130/6475
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dc.contributor.authorMendis, M. J. L.-
dc.date.accessioned2022-02-21T08:48:37Z-
dc.date.available2022-02-21T08:48:37Z-
dc.date.issued2021-
dc.identifier.citationMendis M. J. L. (2021),Automorphisms of Latin Squares,Proceedings of the Annual Research Symposium, 2020, University of Colombo, 366en_US
dc.identifier.urihttp://archive.cmb.ac.lk:8080/xmlui/handle/70130/6475-
dc.description.abstractA Latin Square L of order n is an n×n array containing n symbols from [n] = {1, 2, . . . ,n} such that each element of [n] appears once in each row and each column of L. Rows and columns of L are indexed by elements of [n]. An automorphism α of a Latin square is a permutation such that the triple (α, α, α) maps the Latin square L to itself by permuting its rows, columns and symbols by α. Let Aut(n) be the set of all automorphisms of Latin squares of order n. Whether a permutation α belongs to Aut(n) depends only on the cycle structure of α. Stones et al. [1] characterized α ∈ Aut(n) for which α has at most three non-trivial cycles (that is, cycles other than fixed points). A notable feature of this characterisation is that the length of the longest cycle of α is always divisible by the length of every other cycle of α. In this research we prove a related result for automorphisms with four non-trivial cycles.en_US
dc.language.isoenen_US
dc.publisherUniversity of Colomboen_US
dc.subjectLatin Squareen_US
dc.subjectAutomorphismen_US
dc.subjectCycle Structureen_US
dc.subjectPermutationen_US
dc.titleAutomorphisms of Latin Squaresen_US
dc.typeArticleen_US
Appears in Collections:Department of Mathematics

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