Some applications of the \(q\)-exponential formula
type: Item
instance of: scholarly article
title: Some applications of the \(q\)-exponential formula
zbMATH Open document ID: 0873.05009
DOI: 10.1016/S0012-365X(96)83016-0
author: Warren P. Johnson
published in: Discrete Mathematics
publication date: 1996-10-14T00:00:00Z
review text: The \(q\)-analogue of the well-known exponential formula, which was presented by \textit{I. M. Gessel} [Discrete Math. 40, 69-80 (1982; Zbl 0485.05004)], is given a new combinatorial interpretation. This \(q\)-exponential formula is then used to obtain \(q\)-analogues of Bell numbers and Stirling numbers of the first and second kinds.
reviewed by: M.Oravas
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 11B73
zbMATH DE Number: 935381
zbMATH Keywords: \(q\)-analogue
zbMATH Keywords: \(q\)-exponential formula
zbMATH Keywords: Bell numbers
zbMATH Keywords: Stirling numbers
MaRDI profile type: Publication
cites work: On the Foundations of Combinatorial Theory V, Eulerian Differential Operators
cites work: Q4146776
cites work: The iterated exponential integers
cites work: A unified combinatorial approach for \(q\)- (and \(p,q\)-) Stirling numbers
cites work: Juggling and applications to \(q\)-analogues
cites work: A \(q\)-analog of the exponential formula
cites work: Q5834760
cites work: The q-Stirling numbers of first and second kinds
cites work: Q4040884
cites work: A \(q\)-analogue of Faà di Bruno's formula
cites work: Two Notes on Notation
cites work: A q-Analog of Restricted Growth Functions, Dobinski's Equality, and Charlier Polynomials
cites work: Restricted growth functions, rank row matchings of partition lattices, and q-Stirling numbers
cites work: Q3243274
cites work: The Number of Partitions of a Set
cites work: Congruence properties of \(q\)-analogs
cites work: Q5819726
cites work: Q3855186
cites work: \(p,q\)-Stirling numbers and set partition statistics
cites work: Q3995745
description: scientific article; zbMATH DE number 935381