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Completing partial latin squares with 2 filled rows and 3 filled columns

Authors
  • Göransson, Herman
Publication Date
Jan 01, 2020
Source
DiVA - Academic Archive On-line
Keywords
Language
English
License
Green
External links

Abstract

The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b completed columns and all other cells empty. We identify reductions of partial latin squares in PLS(2, 3; n) by using permutations described by filled rows and intersections of filled rows and columns. We find that all partial latin squares in PLS(2, 3;n), where n is sufficiently large, can be completed if such a reduction can be completed. We also show that all partial latin squares in PLS(2, 3; n) where the intersection of filled rows and columns form a latin rectangle have completions for n ≥ 8.

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