On a partition identity
type: Item
instance of: scholarly article
title: On a partition identity
zbMATH Open document ID: 0532.05003
DOI: 10.1016/0097-3165(84)90012-8
author: Frank Schmidt
author: Rodica Simion
published in: Journal of Combinatorial Theory. Series A
publication date: 1984-01-01T00:00:00Z
review text: Two proofs are given for the identity \(\prod a_1!a_2!\cdots a_n!=\prod 1^{a_1}2^{a_2}\cdots n^{a_n}\), where both products range over \(\sum ia_i=n\), i.e. over all partitions of \(n\). They yield a simple proof of the known formula, \(\det^2T(n) = \left[\prod 1^{a_1}2^{a_2}\cdots n^{a_n}\right]^2\), where \(T(n)\) is the matrix formed by the character table of \(S_n\). Finally a sufficient condition is given so that the permanent of \(T(n)\) is zero.
reviewed by: J. Cigler
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 3843752
zbMATH Keywords: partition identity
zbMATH Keywords: character table
zbMATH Keywords: symmetric group
zbMATH Keywords: formula for determinant
zbMATH Keywords: permanent
MaRDI profile type: Publication
full work available at URL: 0097-3165(84)90012-8
OpenAlex ID: W1991284833
cites work: On representations of the braid group
cites work: Q3859835
cites work: Q4103728
cites work: The representation theory of the symmetric groups
cites work: Invariant theory, tensors and group characters
cites work: Q3947818
cites work: Permanents
description: scientific article; zbMATH DE number 3843752