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Orthogonal Latin Rectangles

Published online by Cambridge University Press:  01 July 2008

ROLAND HÄGGKVIST  and
ANDERS JOHANSSON
ROLAND HÄGGKVIST
Affiliation:
Matematiska Institutionen, Umeå Universitet, S-901 87 Umeå, Sweden (e-mail: rolandh@math.umu.se)
ANDERS JOHANSSON
Affiliation:
N-Institutionen, Högskolan i Gävle, S-801 76 Gävle, Sweden (e-mail: ajj@hig.se)
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Abstract

We use a greedy probabilistic method to prove that, for every ε > 0, every m × n Latin rectangle on n symbols has an orthogonal mate, where m = (1 − ε)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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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 4 , July 2008 , pp. 519 - 536
Copyright
Copyright © Cambridge University Press 2008

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