Latin Squares with No Small Odd Plexes
نویسندگان
چکیده
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 aLatin 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 < n4 but does have a k-plex for every other k ≤ 1 2n. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 477–492, 2008
منابع مشابه
Indivisible partitions of latin squares
In a latin square of order n, a k-plex is a selection of kn entries in which each row, column and symbol occurs k times. A 1-plex is also called a transversal. An indivisible k-plex is one that contains no c-plex for 0ocok. For orders n= 2f2,6g, existence of latin squares with a partition into 1-plexes was famously shown in 1960 by Bose, Shrikhande and Parker. A main result of this paper is tha...
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