Stirling numbers and records

Stirling Numbers and Records

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.

Congruences on Stirling Numbers and Eulerian Numbers

In this paper, we establish some Fleck-Weisman type congruences for the Stirling numbers and the Eulerian numbers.

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...

The p-Stirling Numbers

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