On a generalization of Waring's formula
type: Item
instance of: scholarly article
title: On a generalization of Waring's formula
zbMATH Open document ID: 0899.05069
published in: Advances in Applied Mathematics
publication date: 1998-11-08T00:00:00Z
review text: Waring's formula expresses a power sum symmetric function as a sum of elementary symmetric functions, see \textit{M. P. MacMahon} [Combinatory analysis, Chelsea, New York (1960; Zbl 0101.25102)]. Konvalina has extended this formula to expand an elementary symmetric function in variables \(x^n_1,\dots, x^n_m\) instead of expanding a power sum symmetric function, see \textit{J. Konvalina} [A generalization of Waring's formula, J. Comb. Theory, Ser. A 75, No. 2, 281-294, Art. No. 0078 (1996; Zbl 0857.05094)]. The paper under review shows how, using a simple transformation, Konvalina's result follows directly from Waring's formula. This paper also lists some corrections to Konvalina's paper.
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 1139869
zbMATH Keywords: Waring's formula
zbMATH Keywords: power sum symmetric function
zbMATH Keywords: elementary symmetric functions
author: Jiang Zeng
reviewed by: Angèle. M. Hamel
MaRDI profile type: Publication
full work available at URL: aama.1997.0545
OpenAlex ID: W2064167105
cites work: A generalization of Waring's formula
cites work: Q3947818
cites work: Q3283895
DOI: 10.1006/AAMA.1997.0545
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description: scientific article; zbMATH DE number 1139869