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Latin squares with no small odd plexes
Author(s) -
Egan Judith,
Wanless Ian M.
Publication year - 2008
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20178
Subject(s) - latin square , combinatorics , mathematics , transversal (combinatorics) , square (algebra) , order (exchange) , symbol (formal) , selection (genetic algorithm) , computer science , chemistry , geometry , artificial intelligence , mathematical analysis , rumen , food science , finance , fermentation , economics , programming language
A k ‐plex in a Latin square of order n is a selection of kn entries in which each row, column, and symbol is represented precisely k times. A transversal of a Latin square corresponds to the case k = 1. We show that for all even n > 2 there exists a Latin square of order n which has no k ‐plex for any odd $k < \lfloor {n\over 4} \rfloor$ but does have a k ‐plex for every other $k \le {1\over 2} n$ . © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 477–492, 2008