Avoiding132Permutation

The 132-avoiding permutation of Krattenthaler's bijection, built from the path's area sequence read from the end.

FindStatMp00025via DyckPath↗

Avoiding132Permutation(DyckPath)The 132-avoiding permutation of Krattenthaler's bijection, built from the path's area sequence read from the end.

Typed signatures

Type	Package	Applies
(dyck_path) -> permutation	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a DyckPath and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00025, Sage's to_132_avoiding_permutation. Injective.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{Avoiding132Permutation}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{Permutation}}([3, 1, 2])$

About

Examples	1
Crosswalk	FindStat