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Comment on a Note by J. Marica and J. Schönheim

Published online by Cambridge University Press:  20 November 2018

Charles C. Lindner
Charles C. Lindner*
Affiliation:
Auburn University, Auburn, Alabama
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In [2] it is shown that an n × n partial latin square with n — 1 cells occupied on the main diagonal can be completed to a latin square. We can use the technique in [2] to prove the following result.

An n × n partial latin square with n — 1 cells occupied with n — 1 distinct symbols can be completed to a latin square if the occupied cells are in different rows or different columns.

Let P be an n × n partial latin square based on 0,1, 2, …, n — 1 satisfying the above conditions, and let (x0, y0), (x1, y1), …, (xn-2, yn-2) De the occupied cells where y0, y1, … yn-2 are distinct.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 539
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Hall, M. Jr., A combinatorial problem on abelian groups, Proc. Amer. Math. Soc. 3 (1952), 584-587.Google Scholar
2. Marica, J. and Schönheim, J., Incomplete diagonals of latin squares, Canad. Math. Bull. 12 (1969), p. 235.Google Scholar