PeaksToValleys

The path with a valley wherever the original has a peak of height at least 2, each valley two lower than its peak.

FindStatMp00222via DyckPath↗

PeaksToValleys(DyckPath)The path with a valley wherever the original has a peak of height at least 2, each valley two lower than its peak.

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 Mp00222, the inverse of rowmotion on Dyck paths as order ideals of the triangular poset.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat