Geodesic
Incomplete Diagonals of Latin Squares
Canadian mathematical bulletin, Tome 12 (1969) no. 2, p. 235

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Marica, J.; Schönheim, J. Incomplete Diagonals of Latin Squares. Canadian mathematical bulletin, Tome 12 (1969) no. 2, p. 235. doi: 10.4153/CMB-1969-030-5
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[1] 1. Hall, M. Jr, A combinatorial problem on abelian groups. Proc. Amer. Math. Soc. 3 (1952) 584–587. Google Scholar

[2] 2. Dénes, J., Lecture at University of Surrey, 1967. Google Scholar

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