FoataInversionsToMajor from BinaryWord
The inverse of Foata's bijection on words: peel off the last letter, rotate the blocks of the rest back.
FindStat's Mp00316.
Called as CombinatorialMap(x, "FoataInversionsToMajor"). The head's page has its examples.
Live
Explore
Each element of BinaryWord at a size, and its image, applied in your browser; sizes past 6 are not offered.
Properties
Transport a statistic
Pick a statistic on BinaryWord. Its distribution over the images of BinaryWord at each size is computed, and compared with the 59 statistics on BinaryWord: 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, IntegerComposition.
FindStat Mp00316
inverse Foata bijection
Matched by value: our map agrees with FindStat's image on each of the 126 rows of size at most 6 we can read (0 unread; its table has 1074 rows).
BijectionGraded mapas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
0 | 0 |
1 | 1 |
00 | 00 |
01 | 01 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00316 has the rest.