IntertwiningToDualMajorIndex

The set partition whose growth word is the intertwining word: a bijection taking the intertwining number to the dual major index.

FindStatMp00171via SetPartition↗

IntertwiningToDualMajorIndex(SetPartition)The set partition whose growth word is the intertwining word: a bijection taking the intertwining number to the dual major index.

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 Mp00171, the inverse of DualMajorIndexToIntertwining. Entry i of the intertwining word counts the arcs crossing the one that ends at i.

Examples

Basic #

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

live ↗

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

About

Examples	1
Crosswalk	FindStat