@article{d1249827c9ab4475960997782777cd10,
title = "Birkhoff-von Neumann Theorem for Multistochastic Tensors",
abstract = "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",
author = "Cui, {Lu Bin} and Wen Li and Ng, {Michael K.}",
note = "Funding information: t School of Mathematical Sciences, South China Normal University, Guangzhou, China (hnzkc@ 163.com,
[email protected]). The first author was supported by the Scientific Research Foundation of Graduate School of South China Normal University (2013kyjj010). The second author was supported by NSF of Guangdong province (520130100112530, 52012010009985), NNSF of China (0971075. ll2Tll44), Research Fund for the Doctoral Program of Higher Education of China (2010440711000ll), and Project of Department of Education of Guangdong Province (2013KJCX0053). t Centre for Mathematical Imaging and Vision, and Department of Mathematics, Hong Kong Baptist University, Hong Kong (
[email protected]). This author was supported in part by RGC GRF grant 201812. Publisher copyright: {\textcopyright} 2014, Society for Industrial and Applied Mathematics",
year = "2014",
month = jul,
day = "17",
doi = "10.1137/120896499",
language = "English",
volume = "35",
pages = "956--973",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "3",
}