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arXiv · 2207.08116

Support of extremal doubly stochastic arrays

Mark Mordechai Etkind·Nir Lev
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Abstract

An $n \times m$ array with nonnegative entries is called doubly stochastic if the sum of its entries at each row is $m$ and at each column is $n$. The set of all $n \times m$ doubly stochastic arrays is a convex polytope with finitely many extremal points. The main result of this paper characterizes the possible sizes of the supports of all extremal $n \times m$ doubly stochastic arrays. In particular we prove that the minimal size of the support of an $n \times m$ doubly stochastic array is $n + m - \gcd(n,m)$. Moreover, for $m=kn+1$ we also characterize the structure of the support of the extremal arrays.

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BibTeXRIS

Mark Mordechai Etkind, Nir Lev. 2022-07-17. Support of extremal doubly stochastic arrays. https://arxiv.org/abs/2207.08116

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