A remarkable multiple analogue of the Stirling numbers of the first and second kind was recently constructed by the author. Certain summation identities, and related properties of this family of multiple special numbers are investigated in the present paper.

The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.

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...

A Stirling number of the second kind is a combinatorial function which yields interesting number theoretic properties with regard to primality. The Stirling number of the second kind, S(n; k) = 1 k! k P i=0 ( 1) k i (k i), counts the number of partitions of an n-element set into k non-empty subsets. A Stirling prime (of the second kind) is a prime p such that p = S(n; k) for some integers n and...