SupportDyckPath

The Dyck path whose area sequence is j minus the j-th smallest entry: the parking function's support.

FindStatMp00056via ParkingFunction↗

SupportDyckPath(ParkingFunction)The Dyck path whose area sequence is j minus the j-th smallest entry: the parking function's support.

Typed signatures

Type	Package	Applies
(parking_function) -> dyck_path	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a ParkingFunction and returns a DyckPath — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00056, Sage's to_area_sequence. A surjection: the preimage of a path is its parking functions, the labelings of its up steps.

Examples

Basic #

the parking function $2113$

live ↗

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

About

Examples	1
Crosswalk	FindStat