BouncePath

The bounce path of a Dyck path, bouncing between the path and the diagonal from the far corner.

FindStatMp00099via DyckPath↗

BouncePath(DyckPath)The bounce path of a Dyck path, bouncing between the path and the diagonal from the far corner.

Typed signatures

Type	Package	Applies
(dyck_path) -> dyck_path	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a DyckPath and returns a DyckPath — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00099, the first half of the zeta map. Idempotent: a bounce path is its own bounce path.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{BouncePath}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0])$

About

Examples	1
Crosswalk	FindStat