Comparison of the upper bounds for the extreme points of the polytopes of line-stochastic tensors

We call a real multi-dimensional array a {\em tensor} for short. In enumerating vertices of the polytopes of stochastic tensors, different approaches have been used: {(1)} Combinatorial method via Latin squares; {(2)} Analytic (topological) approach by using hyperplanes; {(3)} Computational geometry...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Zhang, Fuzhen, Xiao-Dong, Zhang
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.11.2021
Subjects
Apexes
Arrays
Combinatorial analysis
Computational geometry
Enumeration
Hyperplanes
Linear programming
Mathematical analysis
Optimization
Polytopes
Tensors
Upper bounds
Online AccessGet full text

Cover

More Information
Summary:We call a real multi-dimensional array a {\em tensor} for short. In enumerating vertices of the polytopes of stochastic tensors, different approaches have been used: {(1)} Combinatorial method via Latin squares; {(2)} Analytic (topological) approach by using hyperplanes; {(3)} Computational geometry (polytope theory) approach; and (4) Optimization (linear programming) approach. As all these approaches are worthy of consideration and investigation in the enumeration problem, various bounds have been obtained. This note is to compare the existing upper bounds arose from different approaches.
ISSN:2331-8422