#
Latin squares with no small odd plexes

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 < floor(n/4) but does
have a k-plex for every other k up to n/2.
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