论文标题
双向随机阵列，并带有少量支撑
Doubly stochastic arrays with small support
论文作者
论文摘要
$ n \ times m $非负矩阵，带有行和$ m $，列$ n $称为双重随机矩阵。我们回答了为每$ 1 <n \ leq m $提供最小的合格支持的双随机矩阵的问题。任何最低支持的矩阵在凸度的性质上都是极端的，而不提供最小支持的极端矩阵的示例。但是，当$ n时，m $是副整体矩阵，恰好是最低支持的矩阵。
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 $1 <n \leq m$. 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.
