PrimeDyckPath

The path wrapped in one more up step first and down step last: a path that touches the diagonal only at its ends.

FindStatMp00199via DyckPath↗

PrimeDyckPath(DyckPath)The path wrapped in one more up step first and down step last: a path that touches the diagonal only at its ends.

Typed signatures

Type	Package	Applies
(dyck_path) -> dyck_path	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a DyckPath and returns a DyckPath — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00199. Injective, one semilength up; the paths it reaches are those with a single return.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{PrimeDyckPath}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{DyckPath}}([1, 1, 1, 0, 0, 1, 0, 0])$

About

Examples	1
Crosswalk	FindStat