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On a result of S. Sherman concerning doubly stochastic matrices

On a result of S. Sherman concerning doubly stochastic matrices

He also defines, following Hardy, Littlewood and Polya [3 ] a partial ordering of n-dimensional real vectors: a <b if, and only if, there exists a d.s. matrix P such that a = Pb. In the above named article, the author investigates a conjecture of S. Kakutani to the effect …