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

Thumbnail Image

Departments

School / College / Institute

Program

KU Authors

Co-Authors

Donovan, Diane
Grannell, Mike

Publication Date

Language

Embargo Status

NO

Journal Title

Journal ISSN

Volume Title

Alternative Title

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 16n2 which has at least 2n mutually orthogonal mates. Further, for any t⩾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(n2)⩾N(n)+2. In particular, it follows that N(576)⩾9, improving the previously known lower bound N(576)⩾8.

Source

Publisher

Elsevier

Subject

Mathematics

Citation

Has Part

Source

Discrete Mathematics

Book Series Title

Edition

DOI

10.1016/j.disc.2020.111835

item.page.datauri

Link

Rights

Copyrights Note

Endorsement

Review

Supplemented By

Referenced By

0

Views

5

Downloads

View PlumX Details