LeftToRightMaximaDyckPath

The Dyck path whose rises climb to each left-to-right maximum and whose falls run to the next one.

FindStatMp00127via Permutation↗

LeftToRightMaximaDyckPath(Permutation)The Dyck path whose rises climb to each left-to-right maximum and whose falls run to the next one.

Typed signatures

Type	Package	Applies
(permutation) -> dyck_path	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a Permutation and returns a DyckPath — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00127. Restricted to the 321-avoiding permutations it is a bijection with the Dyck paths.

Examples

Basic #

the one-line word $231$

live ↗

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

About

Examples	1
Crosswalk	FindStat