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.

URL: https://ajc.maths.uq.edu.au/pdf/67/ajc_v67_p352.pd...

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.

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About

• Item ORO ID
• 46376
• Item Type
• Journal Item
• ISSN
• 1034-4942
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  The Open University	Not Set	Not Set
  University of Queensland Raybould Visiting Fellowship	Not Set	Not Set

• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Related URLs
• • http://arxiv.org/abs/1504.08101(Other)
  • http://ajc.maths.uq.edu.au/?page=home(Other)
• Depositing User
• Bridget Webb