TouchPointCount

Points where the path touches the axis — the returns.

TouchPointCount(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.
• The catalog carries both spellings; they are the same statistic, which is why both are defined rather than one aliased to the other.

Examples