Two recurrence relations for Stirling factors
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.
isomorphism classes of phylogenetic trees
scientific article; zbMATH DE number 1421349