Complement from IntegerComposition
The composition cut exactly where this one is not: its cut set complemented.
Reverse then complement is TransposeComposition, and reversing commutes with complementing.
Called as CombinatorialMap(x, "Complement"). The head's page has its examples.
Live
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.
Also from
The same name out of other carriers, each its own implementation: Permutation, SignedPermutation, SetPartition, SetComposition, BinaryWord.
FindStat Mp00039
complement
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/Mp00039 has the rest.