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Ars Combinatoria

  • Research article

Latin Squares: Critical Sets and their Lower Bounds

Diane Donovan1, Joan Cooper2, D.J. Nott3, Jennifer Seberry4
1 Information Security Research Centre, Faculty of Information Technology Queensland University of Technology Queensland, Australia 4001
2 Department of Information and Communication Technology University of Wollongong Wollongong, Australia 2522
3 Centre for Combinatorics, Mathematics Department The University of Queensland Queensland, Australia 4072
4 Centre for Computer Security Research, Computer Science Department University of Wollongong Wollongong, Australia 2522
  • Published: 30/04/1995

Abstract

In this paper we establish a number of new lower bounds on the size of a critical set in a latin square. In order to do this we first give two results which give critical sets for isotopic latin squares and conjugate latin squares. We then use these results to increase the known lower bound for specific classes of critical sets. Finally, we take a detailed look at a number of latin squares of small order. In some cases, we achieve an exact lower bound for the size of the minimal critical set.

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Citation
Diane Donovan, Joan Cooper, D.J. Nott, Jennifer Seberry. Latin Squares: Critical Sets and their Lower Bounds[J], Ars Combinatoria, Volume 039. 33-48. DOI: .