TransposeComposition from IntegerComposition
The conjugate composition: its ribbon shape transposed, the complement of the reverse.
FindStat's "conjugate" on compositions, named for TransposePartition and TransposeTableau: Conjugate is already the complex conjugate. hopf's ConjugateComposition is the same operation on a plain list of parts.
Called as CombinatorialMap(x, "TransposeComposition"). The head's page has its examples.
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Explore
Each element of IntegerComposition at a size, and its image, applied in your browser; sizes past 6 are not offered.
Properties
Transport a statistic
Pick a statistic on IntegerComposition. Its distribution over the images of IntegerComposition at each size is computed, and compared with the 44 statistics on IntegerComposition: those that share it are the ones the map sends it to, as far as the sizes computed show.
FindStat Mp00041
conjugate
Matched by value: our map agrees with FindStat's image on each of the 63 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/Mp00041 has the rest.