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Small Partial Latin Squares that Cannot be Embedded in a Cayley Table

Wanless, Ian M. and Webb, Bridget S. (2017). Small Partial Latin Squares that Cannot be Embedded in a Cayley Table. Australasian Journal of Combinatorics, 67(2) pp. 352–363.

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Abstract

We answer a question posed by Dénes and Keedwell that is equivalent to the following. For each order n what is the smallest size of a partial latin square that cannot be embedded into the Cayley table of any group of order n? We also solve some variants of this question and in each case classify the smallest examples that cannot be embedded. We close with a question about embedding of diagonal partial latin squares in Cayley tables.

Item Type: Journal Item
ISSN: 1034-4942
Project Funding Details:
Funded Project NameProject IDFunding Body
The Open UniversityNot SetNot Set
University of Queensland Raybould Visiting FellowshipNot SetNot Set
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 46376
Depositing User: Bridget Webb
Date Deposited: 23 May 2016 14:41
Last Modified: 23 May 2019 20:31
URI: http://oro.open.ac.uk/id/eprint/46376
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