Geodesic
When is an Incomplete 3 × n Latin Rectangle Completable?
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 57-69

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We use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete 3 × n latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4.
Keywords: incomplete latin rectangle, completability, solution space enumeration, branch-and-bound 
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Euler, Reinhardt; Oleksik, Paweł. When is an Incomplete 3 × n Latin Rectangle Completable?. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 57-69. http://geodesic.mathdoc.fr/item/DMGT_2013_33_1_a5/