Generalized Stirling transform

Stirling Numbers and Generalized Zagreb Indices

We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.

Generalized Stirling and Lah numbers

The theory of modular binomial lattices enables the simultaneous combinatorial analysis of finite sets, vector spaces, and chains. Within this theory three generalizations of Stifling numbers of the second kind, and of Lah numbers, are developed. 1. Stirling numbers and their formal generalizations The nota t ional convent ions of this paper are as follows: N = {0,1,2 . . . . }, P = {1,2,. . . ...

On Extended Generalized Stirling Pairs

Note that the pair of Stirling numbers of the first and second kind is a special case of a GSP [g(t) = e>-l,f(t) = 1n(l + t)]. In the present paper, we define an extended generalized Stirling pair, say {B^n^h), B2{n,k)}, which covers in particular the above known results and other interesting pairs of numbers with combinatorial interpretations. Moreover, similar relations to the orthogonality o...

Combinatorially interpreting generalized Stirling numbers

The Stirling numbers of the second kind { n k } (counting the number of partitions of a set of size n into k non-empty classes) satisfy the relation

Generalized higher order Stirling numbers