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 L n 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.
| Original language | American English |
|---|---|
| Pages (from-to) | 386-393 |
| Number of pages | 8 |
| Journal | Annals of Functional Analysis |
| Volume | 7 |
| Issue number | 3 |
| DOIs | |
| State | Published - Aug 1 2016 |
Bibliographical note
Publisher Copyright:© 2016 by the Tusi Mathematical Research Group.
ASJC Scopus Subject Areas
- Analysis
- Algebra and Number Theory
Keywords
- Doubly stochastic matrix
- Extreme point
- Polytope
- Stochastic semi-magic cube
- Stochastic tensor
Disciplines
- Mathematics
- Physical Sciences and Mathematics
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