Bounce

The bounce statistic, which walks the path bouncing off its own peaks.

FindStatSt000005via DyckPath↗

Bounce(path)

Domain: Dyck path statistics

Details

• Defined over `DyckPath` as an expression in `_x`, evaluated by compute-engine — the definition IS the implementation.
• Takes a `DyckPath` and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
• Equidistributed with Area: (Bounce, Area) and (Area, Dinv) share the same bivariate distribution (see dyck.test.ts).

Examples