Polytopes of Stochastic Tensors

Authors

Haixia Chang
Vehbi Emrah Paksoy, Nova Southeastern UniversityFollow
Fuzhen Zhang, Nova Southeastern UniversityFollow

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

Comments

©2016 by the Tusi Mathematical Research Group

NSUWorks Citation

Chang, Haixia; Paksoy, Vehbi Emrah; and Zhang, Fuzhen, "Polytopes of Stochastic Tensors" (2016). Mathematics Faculty Articles. 205.
https://nsuworks.nova.edu/math_facarticles/205

DOI

10.1215/20088752-3605195