Department of Mathematics
Birkhoff--von Neumann Theorem for Multistochastic Tensors
© 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.
Doubly stochastic matrices, Multistochastic tensors, Permanent, Permutation tensors
Source Publication Title
SIAM Journal on Matrix Analysis and Applications
Society for Industrial and Applied Mathematics
Cui, Lu-Bin, Wen Li, and Michael K. Ng. "Birkhoff--von Neumann Theorem for Multistochastic Tensors." SIAM Journal on Matrix Analysis and Applications 35.3 (2014): 956-973.