Avoiding partial Latin squares
by
Jaromy Kuhl
University of West Florida
Coauthors: Tristan Denley

Let P be an nxn array of symbols. P is called avoidable if for every set of n symbols, there is an nxn Latin square L on these symbols so that corresponding cells in L and P differ. We show that all partial Latin squares of odd order at least 9 are avoidable. This confirms a conjecture of Chetwynd and Rhodes (who showed that all partial Latin squares of even order at least four are avoidable) that says all partial Latin squares of order at least 4 are avoidable. We also consider the following question: given an nxn partial Latin square P with some specified structure, is there an nxn Latin square L of the same structure for which L avoids P? We answer this question in the context of generalized suduko squares.

Date received: March 27, 2009