ZetaMap

The zeta map: the area sequence read backwards, level by level from the top, as ups and downs.

FindStatMp00030via DyckPath↗

ZetaMap(DyckPath)The zeta map: the area sequence read backwards, level by level from the top, as ups and downs.

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.
• Sends the bistatistic (area, dinv) to (bounce, area). FindStat's Mp00030; its inverse is Mp00032.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat