Complement from SetComposition
Each element i replaced by n + 1 - i, the blocks staying in their order.
FindStat's Mp00289.
Called as CombinatorialMap(x, "Complement"). The head's page has its examples.
Live
Explore
Each element of SetComposition at a size, and its image, applied in your browser; sizes past 6 are not offered.
Properties
Transport a statistic
Pick a statistic on SetComposition. Its distribution over the images of SetComposition at each size is computed, and compared with the 0 statistics on SetComposition: those that share it are the ones the map sends it to, as far as the sizes computed show.
No statistic is declared on SetComposition.
Also from
The same name out of other carriers, each its own implementation: Permutation, SignedPermutation, SetPartition, IntegerComposition, BinaryWord.
FindStat Mp00289
complement
Matched by value: our map agrees with FindStat's image on each of the 1200 rows of size at most 6 we can read (0 unread; its table has 1200 rows).
Graded mapInvolutionas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
[{1}] | [{1}] |
[{1,2}] | [{1,2}] |
[{1,2,3}] | [{1,2,3}] |
[{1},{2}] | [{2},{1}] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00289 has the rest.