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A census of critical sets in the latin squares of order at most six
by
Richard Bean
Department of Mathematics, University of Queensland, Australia
Coauthors: Peter Adams (Department of Mathematics, University of Queensland, Australia), Abdollah Khodkar (Department of Mathematics, University of Queensland, Australia)
A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. We find all the critical sets of different sizes in the latin squares of order at most six. We discuss interesting properties concerning the greatest common denominators of the numbers of critical sets obtained, and the ratio of critical sets to isotopy classes to main classes. A construction for a critical set of size \frac(n2-n)2+1 for n >= 6 will be given.
Date received: November 9, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafn-43.