Weakly Completable Sets in Latin Squares

D. R. B. Burgess1
1 Department of Mathematics and Statistics University of Surrey Guildford, Surrey GU2 5XH, UK.

Abstract

Until quite recently, very few weakly completable critical sets were known. The purpose of this note is to prove the existence of at least one Latin square of each order greater than four in which a weakly completable set exists. This is done by actual construction of such a square. Non-existence of weakly completable sets in Latin squares of orders 2, 3, and 4 is already known.