NoncrossingPartition

Biane's noncrossing set partition: the up steps whose matching downs lie in one run of downs form a block.

FindStatMp00138via DyckPath↗

NoncrossingPartition(DyckPath)Biane's noncrossing set partition: the up steps whose matching downs lie in one run of downs form a block.

Typed signatures

Type	Package	Applies
(dyck_path) -> set_partition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a DyckPath and returns a SetPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00138. Injective: it reaches exactly the noncrossing partitions.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

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

About

Examples	1
Crosswalk	FindStat