CompositionBouncePath

The Dyck path that bounces off the diagonal once for each part: a run of that many ups, then as many downs.

FindStatMp00231via IntegerComposition↗

CompositionBouncePath(IntegerComposition)The Dyck path that bounces off the diagonal once for each part: a run of that many ups, then as many downs.

Typed signatures

Type	Package	Applies
(composition) -> dyck_path	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a IntegerComposition and returns a DyckPath — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00231. An injection; the paths it reaches are those made of runs of as many downs as ups.

Examples

Basic #

the composition $2 + 1 + 3$

live ↗

In$\mathrm{CompositionBouncePath}({\operatorname{IntegerComposition}}([2, 1, 3]))$Out${\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0])$

About

Examples	1
Crosswalk	FindStat