A Dyck Path is a staircase-like path that starts at the origin in a coordinate system and consists of steps that move either up or to the right. Specifically, each step up is represented as an upward move (U) and each step to the right as a rightward move (R). The path must never go below the horizontal axis, ensuring that the number of upward moves is always greater than or equal to the number of rightward moves at any point along the path. Dyck paths are closely related to several combinatorial structures, including Catalan numbers, which count the number of distinct Dyck paths of a given length. They also have applications in various fields such as computer science, where they can represent valid sequences of parentheses, and in algebraic geometry, where they help in understanding certain types of polytopes.