ReflectParallelogramPolyomino

Reflect the path's parallelogram polyomino across the diagonal, so the first column becomes the first row.

FindStatMp00228via DyckPath↗

ReflectParallelogramPolyomino(DyckPath)Reflect the path's parallelogram polyomino across the diagonal, so the first column becomes the first row.

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 Mp00228, an involution: it swaps each adjacent pair of steps from the second step on.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat