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.
| Original language | American English |
|---|---|
| Pages (from-to) | 701-713 |
| Number of pages | 13 |
| Journal | Acta Mathematica Vietnamica |
| Volume | 43 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 8 2018 |
Bibliographical note
Publisher Copyright:© 2018, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.
Funding
Funding Information The work of Wang was partially supported by the Natural Science Foundation of China (11571220); the work of Zhang was partially supported by an NSU PFRDG Research Scholar grant.
| Funders | Funder number |
|---|---|
| Nova Southeastern University | |
| National Natural Science Foundation of China | 11571220 |
ASJC Scopus Subject Areas
- General Mathematics
Keywords
- Birkhoff-von Neumann theorem
- Doubly stochastic matrix
- Hypermatrix
- Matrix of higher order
- Multidimensional array
- Permanent
- Polytope
- Stochastic tensor
- Tensor
Disciplines
- Mathematics
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