Two recurrence relations for Stirling factors
type: Item
instance of: scholarly article
title: Two recurrence relations for Stirling factors
zbMATH Open document ID: 0967.05006
author: Jean Pedersen
author: Peter Hilton
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2001-08-30T00:00:00Z
review text: Stirling factors, \(\mu_{hk}\), are defined by the formula \[ P(m,m-k)= \sum^k_{h=0} {m\choose h+k}\mu_{hk} \] where \(P(m,n)\) is the number of partitions of a set of \(m\) objects into \(n\) mutually disjoint nonempty subsets. The authors supply a combinatorial interpretation for Stirling factors and derive two recurrence relations for them. They then use one of these recurrence relations to provide a simple proof of a relationship between Stirling factors \(\mu_{hk}\) and the number of isomorphism classes of phylogenetic trees with \(k+2\) labelled leaves and \(h\) internal nodes of degree at least three.
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 1421349
zbMATH Keywords: Stirling factors
zbMATH Keywords: recurrence relations
zbMATH Keywords: isomorphism classes of phylogenetic trees
reviewed by: Angèle. M. Hamel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1421349