Doubly stochastic arrays with small support

Abstract

An $n\times m$ non-negative matrix with row sum $m$ and column sum $n$ is called doubly stochastic. We answer the problem of finding doubly stochastic matrices of smallest posible support for every $1<n\le m$. Any matrix of minimum support is extremal in the sence of convexity, while examples of extremal matrices that are not of minimum support are given. But when $n,m$ are coprime integers extremal matrices are precisely those of minimum support.

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