BilleyJockuschStanleyPermutation

The 321-avoiding permutation with entry (ups through a valley) + 1 at the position of its downs through that valley: the Billey-Jockusch-Stanley bijection.

FindStatMp00129via DyckPath↗

BilleyJockuschStanleyPermutation(DyckPath)The 321-avoiding permutation with entry (ups through a valley) + 1 at the position of its downs through that valley: the Billey-Jockusch-Stanley 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 Mp00129. The other entries fill the remaining positions increasingly. Injective: it reaches the 321-avoiding permutations.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat