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On Smetaniuk's Construction for Latin Squares and the Andersen–Hilton Theorem
Author(s) -
Damerell R. M.
Publication year - 1983
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-47.3.523
Subject(s) - latin square , mathematics , square (algebra) , discrete mathematics , algebra over a field , pure mathematics , geometry , chemistry , rumen , food science , fermentation
The Andersen–Hilton theorem gives necessary and sufficient conditions for a latin square of size n × n to be completed if at most n cells are preassigned. This paper uses a construction due to Smetaniuk to give a short proof of this theorem.