AdinBagnoRoichman

The bijection of Adin, Bagno and Roichman on the 321-avoiding permutation of the path, read back as a path: it keeps the ups before each peak.

FindStatMp00124via DyckPath↗

AdinBagnoRoichman(DyckPath)The bijection of Adin, Bagno and Roichman on the 321-avoiding permutation of the path, read back as a path: it keeps the ups before each 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 Mp00124. It sends the number of returns to the number of ups after the last double rise.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat