RskShape from Permutation
The common shape of the RSK tableaux: the row lengths, as a partition of n.
By Schensted, its first part is the longest increasing subsequence and its first COLUMN is the longest decreasing one — two statistics readable off this map.
Called as CombinatorialMap(x, "RskShape"). The head's page has its examples.
Live
FindStat Mp00060
Robinson-Schensted tableau shape
Matched by value: our map agrees with FindStat's image on each of the 873 rows of size at most 6 we can read (0 unread; its table has 1200 rows).
SurjectionGraded mapas FindStat records them, checked by FindStat's contributors.
Sends a permutation to its Robinson-Schensted tableau shape.
| Object | Image |
|---|---|
[1] | [1] |
[1,2] | [2] |
[2,1] | [1,1] |
[1,2,3] | [3] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00060 has the rest.