KnuthKrattenthaler

The 321-avoiding permutation whose left-to-right maxima are the path's peaks, its RSK pair, and the first row of P with the second row of Q as ups.

FindStatMp00296via DyckPath↗

KnuthKrattenthaler(DyckPath)The 321-avoiding permutation whose left-to-right maxima are the path's peaks, its RSK pair, and the first row of P with the second row of Q as ups.

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 Mp00296: Dyck path, to 321-avoiding permutation (Krattenthaler's bijection), to RSK pair, to Dyck path (Knuth).

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat