Geodesic
On the maximal minors of multi-index transport problems
Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 97-102.

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A partial order on the set of multi-index transportation problems is introduced. The order reflects the complexity of the problems. It is associated with the characteristic polynomial of the restriction matrix and allows to solve the problems posed in the title. 
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V. N. Shevchenko. On the maximal minors of multi-index transport problems. Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 97-102. http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a12/

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