Avoiding321Permutation

The 321-avoiding permutation whose RSK pair is the pair of two-row tableaux read off the first and last halves of the path.

FindStatMp00024via DyckPath↗

Avoiding321Permutation(DyckPath)The 321-avoiding permutation whose RSK pair is the pair of two-row tableaux read off the first and last halves of the path.

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 Mp00024. It sends centered tunnels to fixed points and the semilength plus the height of the middle point to twice the longest increasing subsequence. Injective.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{Avoiding321Permutation}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{Permutation}}([3, 1, 2])$

About

Examples	1
Crosswalk	FindStat