LabelingPermutation

The labeling of the parking function's support Dyck path: the positions of the entries, smallest entry first and equal entries left to right.

FindStatMp00055via ParkingFunction↗

LabelingPermutation(ParkingFunction)The labeling of the parking function's support Dyck path: the positions of the entries, smallest entry first and equal entries left to right.

Typed signatures

Type	Package	Applies
(parking_function) -> permutation	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a ParkingFunction and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00055, which it titles labelling permutation; Sage's standard_permutation().inverse(). A surjection.

Examples

Basic #

the parking function $2113$

live ↗

In$\mathrm{LabelingPermutation}({\operatorname{ParkingFunction}}([2, 1, 1, 3]))$Out${\operatorname{Permutation}}([2, 3, 1, 4])$

About

Examples	1
Crosswalk	FindStat