The Permanent Functions of Tensors

Authors

Qing-Wen Wang, Shanghai University - China
Fuzhen Zhang, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

12-8-2018

Publication Title

Acta Mathematica Vietnamica

Keywords

Birkhoff-von Neumann theorem, Doubly stochastic matrix, Hypermatrix, Matrix of higher order, Multidimensional array, Permanent, Polytope, Stochastic tensor, Tensor

ISSN

0251-4184

Volume

43

Issue/No.

4

First Page

701

Last Page

713

Abstract

By a tensor we mean a multidimensional array (matrix) or hypermatrix over a number field. This article aims to set an account of the studies on the permanent functions of tensors. We formulate the definitions of 1-permanent, 2-permanent, and k-permanent of a tensor in terms of hyperplanes, planes, and k-planes of the tensor; we discuss the polytopes of stochastic tensors; at the end, we present an extension of the generalized matrix function for tensors.

Comments

©Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Additional Comments

National Science Foundation of China grant #: 11571220

NSUWorks Citation

Wang, Qing-Wen and Zhang, Fuzhen, "The Permanent Functions of Tensors" (2018). Mathematics Faculty Articles. 262.
https://nsuworks.nova.edu/math_facarticles/262

DOI

10.1007/s40306-018-0268-x