Dyck Path
A Dyck Path is a staircase-like path that starts at the origin of a grid and moves only up or right, never going below the x-axis. It consists of steps that can be represented as a sequence of up steps (U) and right steps (R), where the number of U steps equals the number of R steps. This creates a balanced path that returns to the same horizontal level.
Dyck Paths are closely related to several mathematical concepts, including Catalan numbers, which count the number of distinct Dyck Paths of a given length. They also have applications in combinatorics, computer science, and the study of lattice paths.