Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

Demirkale, Fatih, Donovan, Diane, Hall, Joanne, Khodkar, Abdollah and Rao, Asha (2015) Difference Covering Arrays and Pseudo-Orthogonal Latin Squares. Graphs and Combinatorics, 1-22. doi:10.1007/s00373-015-1649-8


Author Demirkale, Fatih
Donovan, Diane
Hall, Joanne
Khodkar, Abdollah
Rao, Asha
Title Difference Covering Arrays and Pseudo-Orthogonal Latin Squares
Journal name Graphs and Combinatorics   Check publisher's open access policy
ISSN 0911-0119
1435-5914
Publication date 2015-11-30
Year available 2015
Sub-type Article (original research)
DOI 10.1007/s00373-015-1649-8
Open Access Status Not yet assessed
Start page 1
End page 22
Total pages 22
Place of publication Tokyo, Japan
Publisher Springer
Collection year 2016
Language eng
Formatted 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.
Keyword Difference covering array
Latin squares
Pseudo-orthogonal Latin squares
Mutually nearly orthogonal Latin squares
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
 
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