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The Existence of latin squares without orthogonal mates

Wanless, Ian M. and Webb, Bridget S. (2006). The Existence of latin squares without orthogonal mates. Designs, Codes and Cryptography, 40(1) pp. 131–135.

DOI (Digital Object Identifier) Link: http://doi.org/10.1007/s10623-006-8168-9
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Abstract

A latin square is a bachelor square if it does not possess an orthogonal mate; equivalently, it does not have a decomposition into disjoint transversals. We define a latin square to be a confirmed bachelor square if it contains an entry through which there is no transversal. We prove the existence of confirmed bachelor squares for all orders greater than three. This resolves the existence question for bachelor squares.

Item Type: Journal Article
ISSN: 0925-1022
Keywords: Latin square; Bachelor square; MOLS; Transversal; Latin trade
Academic Unit/Department: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 2949
Depositing User: Bridget Webb
Date Deposited: 20 Jun 2006
Last Modified: 02 Aug 2016 12:54
URI: http://oro.open.ac.uk/id/eprint/2949
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