NoncrossingPermutation

The noncrossing permutation Stump's bijection gives the path: the cycles of its touch points, peeled off round by round.

FindStatMp00023via DyckPath↗

NoncrossingPermutation(DyckPath)The noncrossing permutation Stump's bijection gives the path: the cycles of its touch points, peeled off round by round.

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 Mp00023, Sage's to_noncrossing_permutation. Injective: its image is the noncrossing permutations. It sends the area to the number of inversions.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat