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On the number of transversals in a class of Latin squares

Donovan, Diane M. and Grannell, Mike J. (2017). On the number of transversals in a class of Latin squares. Discrete Applied Mathematics (Early view).

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.dam.2017.08.021
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Abstract

Denote by $\mathcal{A}_p^k$ the Latin square of order $n=p^k$ formed by the Cayley table of the additive group $(\mathbb{Z}_p^k,+)$, where $p$ is an odd prime and $k$ is a positive integer. It is shown that for each $p$ there exists $Q>0$ such that for all sufficiently large $k$, the number of transversals in $\mathcal{A}_p^k$ exceeds $(nQ)^{\frac{n}{p(p-1)}}$.

Item Type: Journal Item
Copyright Holders: 2017 Elsevier B.V.
ISSN: 0166-218X
Keywords: Latin square; transversal
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 51621
Depositing User: Mike Grannell
Date Deposited: 16 Oct 2017 08:59
Last Modified: 02 Nov 2017 10:55
URI: http://oro.open.ac.uk/id/eprint/51621
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