Orthogonal latin rectangles

Details Orthogonal latin rectangles Orthogonal latin rectangles

2004-09-21

arxiv.org/abs/math/0409398v3

Mathematics

Combinatorics

Accepted for publication in CPC

Scientific paper

We use a greedy probabilistic method to prove that for every $\epsilon > 0$,
every $m\times n$ Latin rectangle on $n$ symbols has an orthogonal mate, where
$m=(1-\epsilon)n$. That is, we show the existence of a second Latin rectangle
such that no pair of the $mn$ cells receives the same pair of symbols in the
two rectangles.

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