Degenerate weighted Stirling numbers

On degenerate numbers and polynomials related to the Stirling numbers and the Bell polynomials

In this paper, we consider the degenerate numbers Rn(λ) and polynomials Rn(x, λ) related to the Stirling numbers and the Bell polynomials. We also obtain some explicit formulas for degenerate numbers Rn(λ) and polynomials Rn(x, λ). AMS subject classification: 11B68, 11S40, 11S80.

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.

Multi-Restrained Stirling Numbers

Given positive integers n, k, and m, the (n, k)-th mrestrained Stirling number of the first kind is the number of permutations of an n-set with k disjoint cycles of length ≤ m. Inverting the matrix consisting of the (n, k)-th m-restrained Stirling number of the first kind as the (n+1, k +1)-th entry, the (n, k)-th m-restrained Stirling number of the second kind is defined. In this paper, the mu...

Stirling Numbers and Records

The p-Stirling Numbers

The purpose of this article is to introduce p-Stirling numbers of the first and second kinds.