DecompositionReverse

Split a path as U A D B at its first return, and swap the pieces, recursively: U B' D A'.

FindStatMp00101via DyckPath↗

DecompositionReverse(DyckPath)Split a path as U A D B at its first return, and swap the pieces, recursively: U B' D A'.

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 Mp00101, an involution. It is the binary tree's left-right symmetry carried across the Dyck-path bijection.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat