The complementary symmetric functions: Connection constants using negative sets
type: Item
instance of: scholarly article
title: The complementary symmetric functions: Connection constants using negative sets
zbMATH Open document ID: 0918.05099
author: E. Damiani
author: Daniel E. Loeb
author: Ottavio M. D'Antona
published in: Advances in Mathematics
publication date: 1999-08-10T00:00:00Z
review text: Let \(f(x)\) be a rational function in \(x\) of degree \(n\). As the main result of this paper, the coefficients \(c_{k}\) in the expansion \[ f(x)=\sum _{k\geq 0} ^{}c_{k}q_{n-k}(x), \quad\text{where}\quad q_i(x)=\prod _{j=1} ^{i}(x-b_j), \] and where the product has to be read as \(1/\prod _{j=1+i} ^{0}(x-b_j)\) for negative \(i\), are expressed in what are otherwise known as supersymmetric analogues of elementary symmetric functions (in \(\lambda\)-ring language, these are elementary symmetric functions in a difference of two alphabets). In several examples it is shown that special cases yield (if though well-known) identities for Stirling numbers, Lah numbers, and \(q\)-binomial coefficients.
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 1211553
zbMATH Keywords: supersymmetric functions
zbMATH Keywords: connection coefficients
reviewed by: C. Krattenthaler
MaRDI profile type: Publication
full work available at URL: aima.1997.1698
OpenAlex ID: W1964532568
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DOI: 10.1006/AIMA.1997.1698
description: scientific article; zbMATH DE number 1211553