Abel, R.J.R., Cavenagh,N.J. & Kuhl,J. (2013) Induced subarrays of Latin squares without repeated symbols. Electronic Journal of Combinatorics. 20(1).
Permanent Research Commons link: http://hdl.handle.net/10289/7437
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 2x2 subarrays induced contain a repeated symbol. We conjecture that any Latin square of order 2m (where m ≥ 2, with exactly five transposition class exceptions of order 6) has such a partition so that every 2x2 subarray induced contains no repeated symbol. We verify this conjecture by computer when m ≤ 4.
The Electronic Journal of Combinatorics
© 2013, The Authors.