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Original Articles

An interesting face of the polytope of doubly stochastic matrices

Pages 5-18 | Received 02 Jan 1984, Published online: 30 May 2007
 

Abstract

We consider a face of dimension (n 2n)/2 of the polytope of n × n doubly stochastic matrices. We determine the minimum permanent on this face and show that the matrices in which achieve this minimum permanent form a convex polytope whose dimension is asymptotic to the dimension of Several problems and conjectures are proposed.

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