Identifier
Values
[1] => [1,0] => [2,1] => [2,1] => 0
[2] => [1,0,1,0] => [3,1,2] => [3,2,1] => 0
[1,1] => [1,1,0,0] => [2,3,1] => [3,2,1] => 0
[3] => [1,0,1,0,1,0] => [4,1,2,3] => [4,2,3,1] => 0
[2,1] => [1,0,1,1,0,0] => [3,1,4,2] => [4,2,3,1] => 0
[1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => [4,3,2,1] => 0
[4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5,2,3,4,1] => 0
[3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,2,3,4,1] => 0
[2,2] => [1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [5,2,4,3,1] => 0
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [5,4,3,2,1] => 0
[5] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [6,2,3,4,5,1] => 0
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,2,3,4,5,1] => 0
[3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,2,3,4,1] => 0
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [6,2,3,5,4,1] => 1
[2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,5,3,1,2] => 0
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [6,2,5,4,3,1] => 0
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [6,5,3,4,2,1] => 0
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,2,3,4,5,1] => 0
[3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [5,4,3,2,1] => 0
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [5,2,6,4,1,3] => 0
[2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => 0
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [4,6,5,1,3,2] => 0
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [6,2,5,4,3,1] => 0
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [6,5,4,3,2,1] => 0
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,2,3,4,5,1] => 0
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,2,6,4,1,3] => 0
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [6,5,4,3,2,1] => 0
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [6,4,3,2,5,1] => 0
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [6,5,4,3,2,1] => 0
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 0
[] => [] => [1] => [1] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of right ropes of a permutation.
Let $\pi$ be a permutation of length $n$. A raft of $\pi$ is a non-empty maximal sequence of consecutive small ascents, St000441The number of successions of a permutation., and a right rope is a large ascent after a raft of $\pi$.
See Definition 3.10 and Example 3.11 in [1].
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.