Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Birkhoff--von Neumann Theorem for Multistochastic Tensors

Language

English

Abstract

© 2014 Society for Industrial and Applied Mathematics.In this paper, we study the Birkhoff-von Neumann theorem for a class of multistochastic tensors. In particular, we give a necessary and sufficient condition such that a multistochastic tensor is a convex combination of finitely many permutation tensors. It is well-known that extreme points in the set of doubly stochastic matrices are just permutation matrices. However, we find that extreme points in the set of multistochastic tensors are not just permutation tensors. We provide the other types of tensors contained in the set of extreme points.

Keywords

Doubly stochastic matrices, Multistochastic tensors, Permanent, Permutation tensors

Publication Date

2014

Source Publication Title

SIAM Journal on Matrix Analysis and Applications

Volume

35

Issue

3

Start Page

956

End Page

973

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/120896499

Link to Publisher's Edition

http://dx.doi.org/10.1137/120896499

ISSN (print)

08954798

ISSN (electronic)

10957162

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