On the extreme points of slice-stochastic tensors

Abstract

In this paper, we study the properties of extreme points of slice-stochastic tensors, and present an analogue of the Birkhoff–von Neumann theorem for slice-stochastic tensors. Some equivalent characterizations for a slice-stochastic tensor to be an extreme point are presented. The number of permutation tensors is also discussed.

Keywords:

• Tensors
• extreme points
• slice-stochastic tensor
• Birkhoff–von Neumann theorem
• permutation tensors

2010 Mathematics Subject Classifications:

• 15A18
• 15A69

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research supported in part by NNSF of China [grant number 12071159,11671158,11601134,11571095,U1811464], Guangdong Basic and Applied Basic Research Foundation [grant number 2020B1515310013], and Foundation of Henan Educational Committee [grant number 21A110013].