The $t$-successive associated Stirling numbers, $t$-Fibonacci--Stirling numbers, and unimodality

Log-concavity of Stirling Numbers and Unimodality of Stirling Distributions

A series of inequalities involving Stirling numbers of the first and second kinds with adjacent indices are obtained. Some of them show log-concavity of Stirling numbers in three different directions. The inequalities are used to prove unimodality or strong unimodality of all the subfamilies of Stirling probability functions. Some additional applications are also presented.

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.

The p-Stirling Numbers

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

The r-Stirling numbers

The r-Stifling numbers of the first and second kind count restricted permutations and respectively restricted partitions, the restriction being that the first r elements must be in distinct cycles and respectively distinct subsets. The combinatorial and algebraic properties of these numbers, which in most cases generalize similar properties of the regular Stirling numbers, are explored starting...

Stirling Numbers and Records