Some sequences of integers
type: Item
instance of: scholarly article
title: Some sequences of integers
zbMATH Open document ID: 0685.05001
DOI: 10.1016/0012-365X(89)90081-2
author: Peter J. Cameron
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author describes ``a kind of experimental mathematics'' based on two transformations of sequences and a hope that not seldomly new insights are gained when finding instances where a known sequence is transformed into another. The two transformations of a sequence \(x=(x_ n)\) of non- negative integers are defined through operators S and A, where \(Sx=(y_ n)\). \(Ax=(z_ n)\) and \[ 1+\sum_{n\geq 1}y_ nt^ n=\prod_{n\geq 1}(1-t^ n)^{-x_ n} \] \[ 1+\sum_{n\geq 1}z_ nt^ n=(1- \sum_{n\geq 1}x_ nt^ n)^{-1}. \] A number of remarkable observations concerning applications of these two transformations are included in the paper.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 11B34
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 4121998
zbMATH Keywords: enumerating sequence
zbMATH Keywords: generating function
zbMATH Keywords: wreath product
reviewed by: Štefan Porubský
MaRDI profile type: Publication
cites work: Analysis of Variance Models in Orthogonal Designs
cites work: Q5184949
cites work: SOME TREELIKE OBJECTS
cites work: Q3714085
cites work: A Universal Structure for N -Free Graphs
cites work: Asymmetric graphs
cites work: Quantitative universality for a class of nonlinear transformations
cites work: Q5819562
cites work: Ultrafunctions, Projective Function Geometry, and Polynomial Functional Equations
cites work: Orbits of Infinite Permutation Groups
cites work: Infinite Permutation Groups of Rapid Growth
cites work: Q4774085
full work available at URL: 0012-365x(89)90081-2
OpenAlex ID: W2048348126
description: scientific article; zbMATH DE number 4121998