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.

DOI: https://doi.org/10.1016/j.disc.2020.111835

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 $N(576)\ge 8$.

Viewing alternatives

Look up in Google Scholar

Download history

Metrics

Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions

Export

About

CORE (COnnecting REpositories)