Identifier
Values
[1,0,1,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,0,1,0,1,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,0,1,1,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,0,0,1,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,0,1,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,0,1,0,1,0,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,1,0,1,1,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,1,0,0,1,0,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,1,0,1,0,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,1,1,0,1,0,0,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.