BarnabeiCastronuovo

The Schützenberger involution that reverses the canonical decompositions of the two halves of the path.

FindStatMp00123via DyckPath↗

BarnabeiCastronuovo(DyckPath)The Schützenberger involution that reverses the canonical decompositions of the two halves of the path.

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 Mp00123. In each half the up steps the path never returns beneath are the empty pieces of the decomposition.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat