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Title: | Automorphisms of Latin Squares |
Authors: | Mendis, M. J. L. |
Keywords: | Latin Square Automorphism Cycle Structure Permutation |
Issue Date: | 2021 |
Publisher: | University of Colombo |
Citation: | Mendis M. J. L. (2021),Automorphisms of Latin Squares,Proceedings of the Annual Research Symposium, 2020, University of Colombo, 366 |
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. |
URI: | http://archive.cmb.ac.lk:8080/xmlui/handle/70130/6475 |
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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