KrattenthalerPermutation

The 321-avoiding permutation whose left-to-right maxima are the path's peaks: Krattenthaler's bijection.

FindStatMp00119via DyckPath↗

KrattenthalerPermutation(DyckPath)The 321-avoiding permutation whose left-to-right maxima are the path's peaks: Krattenthaler's bijection.

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 Mp00119. The value at a peak is the ups so far and its position the downs so far plus one; the other values fill the other positions increasingly. The first step of KnuthKrattenthaler.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat