The Group of Generalized Stirling Numbers

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,. . . ...

Generalized higher order Stirling numbers

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

Convolution Properties of the Generalized Stirling Numbers and the Jacobi-Stirling Numbers of the First Kind

In this paper, we establish several properties of the unified generalized Stirling numbers of the first kind, and the Jacobi-Stirling numbers of the first kind, by means of the convolution principle of sequences. Obtained results include generalized Vandermonde convolution for the unified generalized Stirling numbers of the first kind, triangular recurrence relation for general Stirling-type nu...