Latin trades on three or four rows

Bean, Richard (2006) Latin trades on three or four rows. Discrete Mathematics, 306 23: 3028-3041. doi:10.1016/j.disc.2005.06.040

Author Bean, Richard
Title Latin trades on three or four rows
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2006
Sub-type Article (original research)
DOI 10.1016/j.disc.2005.06.040
Volume 306
Issue 23
Start page 3028
End page 3041
Total pages 14
Place of publication Amsterdam
Publisher Elsevier Science Bv
Collection year 2006
Language eng
Subject CX
Formatted abstract
Latin trades are closely related to the problem of critical sets in Latin squares. We denote the cardinality of the smallest critical set in any Latin square of order n by scs(n). A consideration of Latin trades which consist of just two columns, two rows, or two elements establishes that scs(n)greater-or-equal, slantedn-1. We conjecture that a consideration of Latin trades on four rows may establish that scs(n) ≥  2n-4. We look at various attempts to prove a conjecture of Cavenagh about such trades. The conjecture is proven computationally for values of n less than or equal to 9. In particular, we look at Latin squares based on the group table of View the MathML source for small n and trades in three consecutive rows of such Latin squares.
Keyword Latin squares
Latin trades
integer programming
Q-Index Code CX

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 1 times in Scopus Article | Citations
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Created: Wed, 15 Aug 2007, 09:44:50 EST