Catalan Identity

Catalan identities involve a set of mathematical formulas related to Catalan numbers, which count specific combinatorial structures like correctly matched parentheses, binary trees, and paths avoiding certain obstacles. These identities reveal relationships between different sums and products of Catalan numbers, showing, for example, how complex structures can be broken down into simpler parts or combined to form new structures. Understanding these identities helps in solving recursive problems and analyzing combinatorial patterns efficiently, providing insights into the inherent structure and symmetry present in various mathematical and computer science applications.