LalanneKreweras

The Lalanne-Kreweras involution: labels of the ups and downs that start a double rise or fall, differenced.

FindStatMp00120via DyckPath↗

LalanneKreweras(DyckPath)The Lalanne-Kreweras involution: labels of the ups and downs that start a double rise or fall, differenced.

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.
• An involution that swaps the number of peaks with the number of double rises, and area-related statistics with their dual. Mp00120.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat