A census of critical sets in the Latin squares of order at most six

Adams, P, Bean, R and Khodkar, A (2003) A census of critical sets in the Latin squares of order at most six. Ars Combinatoria, 68 : 203-223.

Author Adams, P
Bean, R
Khodkar, A
Title A census of critical sets in the Latin squares of order at most six
Journal name Ars Combinatoria   Check publisher's open access policy
ISSN 0381-7032
Publication date 2003
Sub-type Article (original research)
Volume 68
Start page 203
End page 223
Total pages 21
Editor S.A. Vanstone
J. Allson
Place of publication Canada
Publisher Charles Babbage Research Centre
Collection year 2003
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract A critical set in a Latin square of order n is a set of entries from the square which can be embedded in precisely one Latin square of order n, Such that if any element of the critical set. is deleted, the remaining set can be embedded, in more than one Latin square of order n.. In this paper we find all the critical sets of different sizes in the Latin squares of order at most six. We count the number of main and isotopy classes of these critical sets and classify critical sets from the main classes into various strengths. Some observations are made about the relationship between the numbers of classes, particularly in the 6 x 6 case. Finally some examples are given of each type of critical set.
Keyword Mathematics
Size
Q-Index Code C1

 
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