Stirling numbers and a geometric ,structure from voting theory

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.

Stirling Numbers and Records

Rook Theory, Generalized Stirling Numbers and (p, q)-Analogues

In this paper, we define two natural (p, q)-analogues of the generalized Stirling numbers of the first and second kind S(α, β, r) and S(α, β, r) as introduced by Hsu and Shiue [17]. We show that in the case where β = 0 and α and r are nonnegative integers both of our (p, q)-analogues have natural interpretations in terms of rook theory and derive a number of generating functions for them. We al...

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.

A Generalization of Stirling Numbers

are called a weighted Stirling pair if f(g(x)) = g(f(x)) = x, i.e.,/and g are reciprocal. When W(x) = l, B^in.k) and B2(n,k) reduce to a Stirling type pair whose properties are exhibited in [7]. In this paper, we shall present a weighted Stirling pair that includes some previous generalizations of Stirling numbers as particular cases. Some related combinatorial and arithmetic properties are als...