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      Induced subarrays of Latin squares without repeated symbols

      Abel, R. Julian R.; Cavenagh, Nicholas J.; Kuhl, Jaromy
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      Cavenagh Induced subarrays 2013.pdf
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       www.combinatorics.org
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      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: https://hdl.handle.net/10289/7437
      Abstract
      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.
      Date
      2013
      Type
      Journal Article
      Publisher
      The Electronic Journal of Combinatorics
      Rights
      © 2013, The Authors.
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      • Computing and Mathematical Sciences Papers [1454]
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