PathRowmotion from BinaryWord
Rowmotion of the word as a lattice path: the path whose peaks are the original's valleys with an up step appended.
FindStat's Mp00280, a bijection. Not Rowmotion: that reads the word as an order ideal.
Called as CombinatorialMap(x, "PathRowmotion"). 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.
FindStat Mp00280
path rowmotion
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 1200 rows).
BijectionGraded mapas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
0 | 1 |
1 | 0 |
00 | 01 |
01 | 10 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00280 has the rest.