Annals of Functional Analysis

Polytopes of stochastic tensors

Haixia Chang, Vehbi E. Paksoy, and Fuzhen Zhang

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1463684084

Digital Object Identifier
doi:10.1215/20088752-3605195

Mathematical Reviews number (MathSciNet)
MR3506610

Zentralblatt MATH identifier
1347.15040

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

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

Citation

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. https://projecteuclid.org/euclid.afa/1463684084


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