Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T07:07:00.131Z Has data issue: false hasContentIssue false
  • English
  • Français

Critical sets in latin squares: an intriguing problem

Published online by Cambridge University Press:  01 August 2016

Donald Keedwell
Donald Keedwell*
Affiliation:
Department of Mathematics and Statistics, University of Surrey, Guildford GU2 7XH
Get access Rights & Permissions [Opens in a new window]

Extract

A latin square of order n is an n × n array (or matrix) containing n distinct symbols (which are often taken to be the symbols 0, 1, …, n - 1, though any n symbols will do) arranged in such a way that all n of these symbols occur in the n cells of each row and also in the n cells of each column. Such squares occur in many guises: for example, as appropriate field layouts in the statistical design of experiments, as the addition or multiplication tables of groups, as a coding theory device and as a means of representing a finite geometry algebraically.

Type
Articles
Information
The Mathematical Gazette , Volume 85 , Issue 503 , July 2001 , pp. 239 - 244
Copyright
Copyright © The Mathematical Association 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Nelder, J. Critical sets in latin squares, in ‘Problem Corner’, CSIRO Division of Math, and Stats. Newsletter 38 (1977).Google Scholar
2. Keedwell, A. D. A note on critical sets for the elementary abelian 2-group, Utilitas Math., 49 (1996) pp. 69–84.Google Scholar
3. Adams, P. and Khodkar, A. Smallest weak and smallest totally weak critical sets for the latin squares of orders at most seven, Ars combin., to appear.Google Scholar
4. Burgess, D. R. B. Weakly completable critical sets in latin squares, J. Combin. Math. Combin. Comput, 34 (2000) pp. 65–69.Google Scholar
5. Bedford, D. and Johnson, M. Weak uniquely completable sets for finite groups, Bull. London Math. Soc. 32 (2000) pp. 155–162.Google Scholar
6. Keedwell, A. D. Critical sets for latin squares, graphs and block designs: a survey, Congressus Numerantium 113 (1996) pp. 231–245.Google Scholar