KasraouiZeng

The Kasraoui-Zeng involution: exchanges the number of crossings with the number of nestings.

FindStatMp00115via SetPartition↗

KasraouiZeng(SetPartition)The Kasraoui-Zeng involution: exchanges the number of crossings with the number of nestings.

Typed signatures

Type	Package	Applies
(set_partition) -> set_partition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a SetPartition and returns a SetPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00115, defined in Kasraoui and Zeng's "Distribution of crossings, nestings and alignments of two edges in matchings and partitions".

Examples

Basic #

the nesting $\{1,4\} \mid \{2,3\}$

live ↗

In$\mathrm{KasraouiZeng}({\operatorname{SetPartition}}([[1, 4], [2, 3]]))$Out${\operatorname{SetPartition}}([[1, 3], [2, 4]])$

About

Examples	1
Crosswalk	FindStat