Annals of Functional Analysis

Polytopes of stochastic tensors

Haixia Chang, Vehbi E. Paksoy, and Fuzhen Zhang

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Considering n×n×n stochastic tensors (aijk) (i.e., nonnegative hypermatrices in which every sum over one index i, j, or k, is 1), we study the polytope (Ωn) of all these tensors, the convex set (Ln) of all tensors in Ωn with some positive diagonals, and the polytope (Δn) generated by the permutation tensors. We show that Ln is almost the same as Ωn except for some boundary points. We also present an upper bound for the number of vertices of Ωn.

Article information

Ann. Funct. Anal., Volume 7, Number 3 (2016), 386-393.

Received: 18 September 2015
Accepted: 26 November 2015
First available in Project Euclid: 19 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15B51: Stochastic matrices
Secondary: 52B11: $n$-dimensional polytopes

doubly stochastic matrix extreme point polytope stochastic semi-magic cube stochastic tensor


Chang, Haixia; Paksoy, Vehbi E.; Zhang, Fuzhen. Polytopes of stochastic tensors. Ann. Funct. Anal. 7 (2016), no. 3, 386--393. doi:10.1215/20088752-3605195.

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