In this paper, we establish several properties of the unified generalized Stirling numbers of the first kind, and the Jacobi-Stirling numbers of the first kind, by means of the convolution principle of sequences. Obtained results include generalized Vandermonde convolution for the unified generalized Stirling numbers of the first kind, triangular recurrence relation for general Stirling-type nu...

In this paper, we consider generalizations of the Stirling number first and second kind by using a specialization new family symmetric functions. We give combinatorial interpretations for these functions means weighted lattice path tilings. also present some convolutions involving complete elementary Additionally, introduce different families set partitions to modular s-Stirling numbers.

The connection between Stirling numbers of the first kind and records is well-known. Applying this relationship, we derive bounds for the maximum likelihood estimator of the sample size based on the number of observed records. The proof proceeds by a remarkable expression of the mode of the unsigned Stirling numbers of the the first kind due to Hammersley. Moreover, this representation of the m...

and Belief-Based Language Differentiate Joking, Pretending, and Literal Toddler-Directed Speech Elena Hoicka ([email protected]) Psychology Department, University of Stirling, Stirling, FK9 4LA, UK Ruth Campbell ([email protected]) Psychology Department, University of Stirling, Stirling, FK9 4LA, UK

Analysis, design, fabrication, and experimental assessment of a symmetric three-phase free-piston Stirling engine system is discussed in this paper. The system is designed to operate with moderate-temperature heat input that is consistent with solar-thermal collectors. Diaphragm pistons and nylon flexures are considered for this prototype to eliminate surface friction and to provide appropriate...

We give a complete proof of a set of identities (7) proposed recently from calculation of high-energy string scattering amplitudes. These identities allow one to extract ratios among high-energy string scattering amplitudes in the fixed angle regime from highenergy amplitudes in the Regge regime. The proof is based on a signless Stirling number identity in combinatorial theory. The results are ...

Note that B(n) is the n Bell number while S(n, k) is the Stirling number of the second kind. We have translated Spivey’s notation into Riordan’s familiar notation which we find more preferable in our work [5, 6]. The purpose of this note is to offer a short generating function proof of Equation (1). We discuss this proof in Section 2. We also use Spivey’s formula, in conjunction with the Stirli...

We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural three-parameter generalization of the well-known Eulerian numbers. We give the generating function for this new class of numbers and, in the simplest cases, we...

The Stirling numbers of the second kind { n k } (counting the number of partitions of a set of size n into k non-empty classes) satisfy the relation