FoataInversionsToMajor from IntegerComposition
The inverse of Foata's bijection on compositions: peel off the last part, rotate the blocks of the rest back.
FindStat's Mp00315.
Called as CombinatorialMap(x, "FoataInversionsToMajor"). 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, BinaryWord.
FindStat Mp00315
inverse Foata bijection
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 1023 rows).
BijectionGraded mapas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
[1] | [1] |
[2] | [2] |
[3] | [3] |
[4] | [4] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00315 has the rest.