Super ballot numbers (original) (raw)

Combinatorial applications of the special numbers and polynomials

2017

In this paper, by using some families of special numbers and polynomials with their generating functions, we give various properties of these numbers and polynomials. These numbers are related to the well-known numbers and polynomials, which are the Euler numbers, the Stirling numbers of the second kind, the central factorial numbers and the array polynomials. We also discuss some combinatorial interpretations of these numbers related to the rook polynomials and numbers. Furthermore, we give computation formulas for these numbers and polynomials.

CATALAN NUMBERS AND APPLICATIONS

Vision Journal, 2019

Catalan numbers have a significant place and major importance in combinatorics and computer science. They form a sequence of natural numbers that occur in studying astonishingly many combinatorial problems. They appear in the triangulation problem of polygon and polyhedron, binary trees, multiplication ordering, lattice path problem, etc. Today, application of the Catalan numbers we see in engineering in the field of computational geometry, geographic information systems, geodesy, cryptography, and medicine. In the problems of computational geometry, they are generally used in geometric modeling. In cryptography are used in the forming of keys for secure transfer of information. In this study, we consider Catalan numbers, their properties, generating function and related problems with them.

Miscellaneous Formulae for the Certain Class of Combinatorial Sums and Special Numbers

2021

The purpose of this paper is to give some integral formulas, identities and combinatorial sums using the numbers y(n,λ). The obtained results are related to the Bernoulli numbers and their interpolation functions, as well as the Pell numbers, the Harmonic numbers, the alternating Harmonic numbers, the Daehee numbers, and the Catalan-Qi numbers. Moreover, we give answers to some open problems involving the numbers y(n,λ).