| 69074 |
Creator |
80b473f9888b354bf7fee26ec7cc369f |
| 69074 |
Creator |
ext-1e8046404a6b06dee89365e07c70c80d |
| 69074 |
Creator |
ext-24fe2e36a031b8a63095c9e617d32eba |
| 69074 |
Date |
2020-06 |
| 69074 |
Is Part Of |
p0012365X |
| 69074 |
Is Part Of |
repository |
| 69074 |
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 $N(576)\ge 8$. |
| 69074 |
authorList |
authors |
| 69074 |
issue |
6 |
| 69074 |
status |
peerReviewed |
| 69074 |
uri |
http://data.open.ac.uk/oro/document/1057506 |
| 69074 |
uri |
http://data.open.ac.uk/oro/document/1057507 |
| 69074 |
uri |
http://data.open.ac.uk/oro/document/1057508 |
| 69074 |
uri |
http://data.open.ac.uk/oro/document/1057509 |
| 69074 |
uri |
http://data.open.ac.uk/oro/document/1057510 |
| 69074 |
uri |
http://data.open.ac.uk/oro/document/1057511 |
| 69074 |
uri |
http://data.open.ac.uk/oro/document/1057968 |
| 69074 |
volume |
343 |
| 69074 |
type |
AcademicArticle |
| 69074 |
type |
Article |
| 69074 |
label |
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. |
| 69074 |
Title |
Embedding partial Latin squares in Latin squares with many mutually orthogonal mates |
| 69074 |
in dataset |
oro |