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Incomplete Diagonals of Latin Squares

Published online by Cambridge University Press:  20 November 2018

J. Marica  and
J. Schönheim
J. Marica
Affiliation:
University of Calgary, Calgary, Alberta
J. Schönheim
Affiliation:
University of Calgary, Calgary, Alberta
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Extract

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The following question has been asked by J. Dénes [2]: If n - 1 elements of the diagonal of an n × n array are prescribed, is it possible to complete the array to form an n × n latin square?" It is known that if n diagonal elements are given such a completion is not always possible.

That the answer to Dénes' question is yes follows directly from a theorem of M. Hall Jr. [1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 235
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Hall, M. Jr, A combinatorial problem on abelian groups. Proc. Amer. Math. Soc. 3 (1952) 584–587.Google Scholar
2. Dénes, J., Lecture at University of Surrey, 1967.Google Scholar