The Open UniversitySkip to content
 

Embedding partial Latin squares in Latin squares with many mutually orthogonal mates

Donovan, Diane; Grannell, Mike and Yazici, Emine Şule (2020). Embedding partial Latin squares in Latin squares with many mutually orthogonal mates. Discrete Mathematics, 343(6), article no. 111835.

Full text available as:
Full text not publicly available (Accepted Manuscript)
Due to publisher licensing restrictions, this file is not available for public download until 7 February 2021
Click here to request a copy from the OU Author.
DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.disc.2020.111835
Google Scholar: Look up in Google Scholar

Abstract

In this paper it is shown that any partial Latin square of order $n$ can be embedded in a Latin square of order at most $16n^2$ which has at least $2n$ mutually orthogonal mates. Further, for any $t\geq 2$, it is shown that a pair of orthogonal partial Latin squares of order $n$ can be embedded in a set of $t$ mutually orthogonal Latin squares (MOLS) of order a polynomial with respect to $n$. A consequence of the constructions is that, if $N(n)$ denotes the size of the largest set of MOLS of order $n$, then $N(n^2)\geq N(n)+2$. In particular, it follows that $N(576)\ge 9$, improving the previously known lower bound $N(576)\ge 8$.

Item Type: Journal Item
Copyright Holders: 2020 Elsevier
ISSN: 0012-365X
Keywords: Embeddings; Embeddings of partial Latin squares; Orthogonal partial Latin squares; Embeddings of orthogonal partial Latin squares
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 69074
Depositing User: Mike Grannell
Date Deposited: 21 Jan 2020 11:16
Last Modified: 25 Mar 2020 18:21
URI: http://oro.open.ac.uk/id/eprint/69074
Share this page:

Metrics

Altmetrics from Altmetric

Citations from Dimensions

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU