Permanent and determinant
type: Item
instance of: scholarly article
title: Permanent and determinant
zbMATH Open document ID: 0636.15003
DOI: 10.1016/0024-3795(87)90337-5
author: Joachim von zur Gathen
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: This paper gives the bound \(m>\sqrt{2}n-6\sqrt{n}\) as the smallest possible dimension m for which the n-dimensional permanent function might be expressible as an m-dimensional determinant function. The proof uses algebraic geometry studying the singular loci of the permanent and determinant functions. The paper generalizes a well known theorem of \textit{M. Marcus} and \textit{H. Minc} [Illinois J. Math. 5, 376-381 (1961; Zbl 0104.009)].
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 4035986
zbMATH Keywords: p-complete
zbMATH Keywords: singular locus
zbMATH Keywords: dimension
zbMATH Keywords: permanent function
zbMATH Keywords: determinant function
reviewed by: Frank Uhlig
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90337-5
OpenAlex ID: W2040174039
cites work: Feasible arithmetic computations: Valiant's hypothesis
cites work: Q3880849
cites work: On the relation between the determinant and the permanent
cites work: Permanents
cites work: Q4135685
cites work: The complexity of computing the permanent
cites work: Q5798024
description: scientific article; zbMATH DE number 4035986