TransposePartition

The conjugate partition: column i of the Ferrers diagram becomes row i.

FindStatMp00044via IntegerPartition↗

TransposePartition(IntegerPartition)The conjugate partition: column i of the Ferrers diagram becomes row i.

CombinatoricaTransposePartition[IntegerPartition]

Typed signatures

Type	Package	Applies
(integer_partition) -> integer_partition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a IntegerPartition and returns a IntegerPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Entry i of the result counts the parts that are at least i, so it is its own inverse and swaps the number of parts with the largest part. Combinatorica's TransposePartition; FindStat's Mp00044, "conjugate". Wolfram's Conjugate is the complex conjugate, not this map.

Examples

Basic #

the partition $4 + 2 + 1$

live ↗

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

About

Examples	1
Checked against	Combinatorica 1 agree
Crosswalk	FindStatCombinatorica

Implementation

mappedcombinatoricapackages/oracle/src/mappings.ts