CallanSwitch

Callan's involution: switches the first closer with the lesser of the least closer and the second element of the block of 1.

FindStatMp00249via SetPartition↗

CallanSwitch(SetPartition)Callan's involution: switches the first closer with the lesser of the least closer and the second element of the block of 1.

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 Mp00249, a joint symmetry of St000971 and St001784.

Examples

Basic #

the set partition $\{1,3\} \mid \{2\} \mid \{4\}$

live ↗

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

About

Examples	1
Crosswalk	FindStat