Identifier
Values
[1] => [1,0,1,0] => [3,1,2] => 0
[2] => [1,1,0,0,1,0] => [2,4,1,3] => 0
[1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 0
[3] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 0
[2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 0
[1,1,1] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 0
[4] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 0
[3,1] => [1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 1
[2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 0
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 0
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => 1
[3,2] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 0
[3,1,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 0
[2,2,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 0
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => 0
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => 1
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => 1
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 0
[3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 0
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => 1
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 0
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 0
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 0
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => 1
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => 0
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 0
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 0
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 0
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => 1
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 0
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => 0
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 0
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => 0
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => 0
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 0
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 0
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => 0
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => 0
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 0
[] => [] => [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 invisible descents of a permutation.
A visible descent of a permutation $\pi$ is a position $i$ such that $\pi(i+1) \leq \min(i, \pi(i))$. Thus, an invisible descent satisfies $\pi(i) > \pi(i+1) > i$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.