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DC Field | Value | Language |
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dc.contributor.author | Mendis, M. J. L. | - |
dc.date.accessioned | 2022-02-21T08:48:37Z | - |
dc.date.available | 2022-02-21T08:48:37Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Mendis M. J. L. (2021),Automorphisms of Latin Squares,Proceedings of the Annual Research Symposium, 2020, University of Colombo, 366 | en_US |
dc.identifier.uri | http://archive.cmb.ac.lk:8080/xmlui/handle/70130/6475 | - |
dc.description.abstract | A 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.iso | en | en_US |
dc.publisher | University of Colombo | en_US |
dc.subject | Latin Square | en_US |
dc.subject | Automorphism | en_US |
dc.subject | Cycle Structure | en_US |
dc.subject | Permutation | en_US |
dc.title | Automorphisms of Latin Squares | en_US |
dc.type | Article | en_US |
Appears in Collections: | Department of Mathematics |
Files in This Item:
File | Description | Size | Format | |
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Automorphisms of Latin Squares.pdf | 263.37 kB | Adobe PDF | View/Open |
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