Ключевое слово: «catalan numbers»

Solving problems in probability theory requires knowledge of the basics of combinatorics. We often encounter combinatorial problems in everyday life. For example, when playing chess, players create several combinations in their minds and choose the best option. When making a schedule, the head teacher chooses the optimal match between teachers and classroom lessons. Combinatorial problems are solved using computer programs, which made it possible to work with big data. In mathematics, there is a concept of special numbers that have special properties. Among such numbers, the Catalan numbers are of greater interest; with the help of their many constructions, combinatorial problems can be solved. Their relevance is due to the fact that Catalan numbers, being special numbers of the natural series, arising from combinatorial problems, generate a number of other combinatorial problems that need to be solved. In this paper, we will consider Catalan numbers that appear in a wide variety of combinatorial problems. The object of the study is Catalan Numbers.