Latin squares with bounded size of row prefix intersections

Authors:
Grzegorz Malewicz
Affiliations:
Google Inc., Department of Engineering, Mountain View, CA and Department of Computer Science, University of Alabama
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

A latin square is a matrix of size n × n with entries from the set {1 ,..., n}, such that each row and each column is a permutation on {1,...,n}. We show how to construct a latin square such that for any two distinct rows, the prefixes of length h of the two rows share at most about h2/n elements. This upper bound is close to optimal when contrasted with a lower bound derived from the Second Johnson bound [6].