Article
The Permanent Functions of Tensors
Acta Mathematica Vietnamica
Document Type
Article
Publication Date
12-8-2018
Keywords
- Birkhoff-von Neumann theorem,
- Doubly stochastic matrix,
- Hypermatrix,
- Matrix of higher order,
- Multidimensional array,
- Permanent,
- Polytope,
- Stochastic tensor,
- Tensor
Disciplines
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.
Additional Comments
National Science Foundation of China grant #: 11571220
DOI
10.1007/s40306-018-0268-x
Citation Information
Qing-Wen Wang and Fuzhen Zhang. "The Permanent Functions of Tensors" Acta Mathematica Vietnamica Vol. 43 Iss. 4 (2018) p. 701 - 713 ISSN: 0251-4184 Available at: http://works.bepress.com/fuzhen-zhang/171/
©Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018