DyckPaths

The Dyck paths of semilength — balanced up/down words — a lazy family of Catalan many.

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DyckPaths(n)the lattice paths of up- and down-steps that never dip below the axis.

Domain: Collections

Details

A lazy indexed collection; the count is the Catalan number — . See CatalanNumber.
Each element is the step word (1 up, 0 down); drawn as a mountain range. Height, Area, Returns and Hills are Dyck-path statistics.
In bijection with binary trees, triangulations, and non-crossing partitions — all Catalan families.

Enumeration

See also: CatalanNumber, Count, At