CATALAN NUMBERS AND APPLICATIONS

ABSTRACT

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.

Keywords. Catalan numbers, triangulation, lattice path, multiplication ordering and binary tree.