Comment on a Note by J. Marica and J. Schönheim
Canadian mathematical bulletin, Tome 13 (1970) no. 4, p. 539
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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 (x 0, y 0), (x 1, y 1), ..., (x n-2, y n-2) De the occupied cells where y 0, y 1, ... y n-2 are distinct.
Lindner, Charles C. Comment on a Note by J. Marica and J. Schönheim. Canadian mathematical bulletin, Tome 13 (1970) no. 4, p. 539. doi: 10.4153/CMB-1970-101-6
@article{10_4153_CMB_1970_101_6,
author = {Lindner, Charles C.},
title = {Comment on a {Note} by {J.} {Marica} and {J.} {Sch\"onheim}},
journal = {Canadian mathematical bulletin},
pages = {539--539},
year = {1970},
volume = {13},
number = {4},
doi = {10.4153/CMB-1970-101-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-101-6/}
}
[1] 1. Hall, M. Jr., A combinatorial problem on abelian groups, Proc. Amer. Math. Soc. 3 (1952), 584-587. Google Scholar
[2] 2. Marica, J. and Schönheim, J., Incomplete diagonals of latin squares, Canad. Math. Bull. 12 (1969), p. 235. Google Scholar
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