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.
@article{bwmeta1.element.doi-10_7151_dmgt_1648, author = {Reinhardt Euler and Pawe\l\ Oleksik}, title = {When is an Incomplete 3 $\times$ n Latin Rectangle Completable?}, journal = {Discussiones Mathematicae Graph Theory}, volume = {33}, year = {2013}, pages = {57-69}, zbl = {1290.05040}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1648} }
Reinhardt Euler; Paweł Oleksik. When is an Incomplete 3 × n Latin Rectangle Completable?. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 57-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1648/
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