Coefficients of functional compositions often grow smoothly
type: Item
instance of: scholarly article
title: Coefficients of functional compositions often grow smoothly
zbMATH Open document ID: 1158.05303
author: Edward A. Bender
author: E. Rodney Canfield
author: L. Bruce Richmond
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/129706
full work available at URL: v15i1r21.html
review text: Summary: The coefficients of a power series \(A(x)\) are smooth if \(a_{n-1}/a_n\) approaches a limit. If \(A(x)=F(G(x))\) and \(f_n^{1/n}\) approaches a limit, then the coefficients of \(A(x)\) are often smooth. We use this to show that the coefficients of the exponential generating function for graphs embeddable on a given surface are smooth, settling a problem of \textit{C.McDiarmid}, \textit{A. Steger}, and \textit{D.J.A. Welsh} [''Random planar graphs,'' J. Comb. Theory, Ser. B. 93, No.\,2, 187--205 (2005; Zbl 1056.05128)].
Mathematics Subject Classification ID: 05A16
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 5540926
zbMATH Keywords: coefficients of power series
zbMATH Keywords: exponential generating function
zbMATH Keywords: graphs embeddable on a surface
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5540926