SwapReturnsAndLastDescent

An involution exchanging the number of returns with the length of the last descent.

FindStatMp00118via DyckPath↗

SwapReturnsAndLastDescent(DyckPath)An involution exchanging the number of returns with the length of the last descent.

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 Mp00118, the specialization to Dyck paths of the map of Elizalde and Rubey. It keeps the number of ups before each down that is neither a return nor in the last descent.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat