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The Permanent Functions of Tensors
Qing-Wen Wang
,
Fuzhen Zhang
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.