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Mathematics Faculty Articles
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.
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
Comments
©2016 by the Tusi Mathematical Research Group