Avoiding312Permutation

The 312-avoiding permutation of Bandlow and Killpatrick: from the identity, each area-sequence entry swaps neighbouring positions that many times.

FindStatMp00031via DyckPath↗

Avoiding312Permutation(DyckPath)The 312-avoiding permutation of Bandlow and Killpatrick: from the identity, each area-sequence entry swaps neighbouring positions that many times.

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 Mp00031. It sends the area to the number of inversions. Injective.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{Avoiding312Permutation}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{Permutation}}([2, 1, 3])$

About

Examples	1
Crosswalk	FindStat