Mathematics Faculty Articles

Title

Polytopes of Stochastic Tensors

Document Type

Article

Publication Date

8-2016

Publication Title

Annals of Functional Analysis

Keywords

Doubly stochastic matrix, Extreme point, Polytope, Stochastic semi-magic cube, Stochastic tensor

ISSN

2008-8752

Volume

7

Issue/No.

3

First Page

386

Last Page

393

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 LnLn is almost the same as Ωn except for some boundary points. We also present an upper bound for the number of vertices of Ωn.

Comments

©2016 by the Tusi Mathematical Research Group

DOI

10.1215/20088752-3605195

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Peer Reviewed

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