Crossings and embracings of set-partitions and \(q\)-analogues of the logarithm of the Fourier transform
type: Item
instance of: scholarly article
title: Crossings and embracings of set-partitions and \(q\)-analogues of the logarithm of the Fourier transform
zbMATH Open document ID: 0878.05009
DOI: 10.1016/S0012-365X(96)83020-2
author: Alexandru Nica
published in: Discrete Mathematics
publication date: 1998-01-05T00:00:00Z
review text: \textit{I. M. Gessel} [Discrete Math. 40, 69-80 (1982; Zbl 0485.05004)] described a \(q\)-analogue of the exponential formula and \textit{A. Nica} [Commun. Math. Phys. 168, No. 1, 187-207 (1995; Zbl 0818.60096)] studied the \(q\)-analogue of the convolution of probability distributions. Here we see the relation between these two ideas. The \(q\)-analogue of the logarithm of the Fourier transform parallels the \(q\)-analogue of the exponential formula of Gessel. Particular cases along the way turn out to be two \(q\)-versions of the Hermite polynomials (the \(q\)-continuous and \(q\)-discrete polynomials). The methods used, beyong the standard partition arguments and path-counting techniques, include infinite matrices. The technical details can be subtle and intricate.
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 935385
zbMATH Keywords: \(q\)-analogue
zbMATH Keywords: logarithm of the Fourier transform
zbMATH Keywords: exponential formula
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: partition
reviewed by: Gerald L. Alexanderson
MaRDI profile type: Publication
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full work available at URL: s0012-365x(96)83020-2
OpenAlex ID: W2061312072
description: scientific article; zbMATH DE number 935385