TransposePartition from IntegerPartition
The conjugate partition: column i of the Ferrers diagram becomes row i.
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.
Called as CombinatorialMap(x, "TransposePartition"). The head's page has its examples.
Live
FindStat Mp00044
conjugate
Matched by value: our map agrees with FindStat's image on each of the 29 rows of size at most 6 we can read (0 unread; its table has 1200 rows).
BijectionGraded mapInvolutionas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
[1] | [1] |
[2] | [1,1] |
[3] | [1,1,1] |
[4] | [1,1,1,1] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00044 has the rest.