Permanents of d-dimensional matrices
type: Item
instance of: scholarly article
title: Permanents of d-dimensional matrices
zbMATH Open document ID: 0614.15003
DOI: 10.1016/0024-3795(87)90311-9
author: Stephen J. Dow
author: Peter Gibson
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: For an \(n_ 1\times n_ 2\times...\times n_ d\) matrix \(A=(A_{i_ 1i_ 2...i_ d})\) the permanent function is defined by \(per A=\sum \prod^{n_ 1}_{i=1}A_{i\sigma_ 2(i)\sigma_ 3(i)...\sigma_ d(i)},\) where the summation ranges over all one-to-one functions \(\sigma_ k\) from \(\{1,2,...,n_ 1\}\) to \(\{1,2,...,n_ k\}\), \(k=2,3,...,d\). Necessarily for each k, \(n_ k\geq n_ 1\). A particular interest is given to those matrices which are nonnegative and have constant hyperplane sums. Many of the properties of permanents of two- dimensional matrices extend to the higher dimensional matrices.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15B51
zbMATH DE Number: 3993763
zbMATH Keywords: higher dimensional matrices
zbMATH Keywords: permanent function
reviewed by: Richard Sinkhorn
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90311-9
OpenAlex ID: W2079848585
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description: scientific article; zbMATH DE number 3993763