Induced subarrays of Latin squares without repeated symbols (Q1953431)

Summary: We show that for any Latin square \(L\) of order \(2m\), we can partition the rows and columns of \(L\) into pairs so that at most \((m+3)/2\) of the \(2\times 2\) subarrays induced contain a repeated symbol. We conjecture that any Latin square of order \(2m\) (where \(m\geq 2\), with exactly five transposition class exceptions of order 6) has such a partition so that every \(2\times 2\) subarray induced contains no repeated symbol. We verify this conjecture by computer when \(m\leq 4\).