Difference covering arrays and pseudo-orthogonal Latin squares

Demirkale, Fatih, Donovan, Diane, Hall, Joanne, Khodkar, Abdollah, & Rao, Asha (2016) Difference covering arrays and pseudo-orthogonal Latin squares. Graphs and Combinatorics, 32(4), pp. 1353-1374.

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Abstract

A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for one symbol with which it is paired twice and one symbol with which it is not paired at all. A set of t Latin squares, of order n, are said to be mutually pseudo-orthogonal if they are pairwise pseudo-orthogonal. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146.

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ID Code: 90984
Item Type: Journal Article
Refereed: Yes
Keywords: Difference covering array, Latin squares, pseudo-orthogonal Latin squares, mutually nearly orthogonal Latin squares
DOI: 10.1007/s00373-015-1649-8
ISSN: 1435-5914
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) (010104)
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2015 Springer Japan
Copyright Statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-015-1649-8
Deposited On: 04 Dec 2015 01:48
Last Modified: 17 Sep 2016 07:09

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