Identifier
-
Mp00183:
Skew partitions
—inner shape⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤ
Values
[[2,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[2,2],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,2],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[4,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,2],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,2],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,3],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[2,2,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,2,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[2,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,1,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[5,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,2],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[5,2],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[4,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[5,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,3],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,3],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,2,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[4,2,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,1,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,3,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[2,2,2],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,2,2],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[2,2,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,3,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[2,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[2,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,1,1,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[6,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[5,2],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[6,2],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[5,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[6,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[4,3],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[5,3],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[4,3,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,2,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[5,3,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[5,2,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[4,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[5,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[4,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,1,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[5,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[4,4],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,3,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,4,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[4,3,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,3,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,2,2],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,3,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[4,2,2],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,3,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,2,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,3,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[4,2,1,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,2,2,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[4,2,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,2,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,1,1,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[4,2,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,3,2],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,3,1,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[3,3,3],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[2,2,2,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,3,2,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,2,2,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[2,2,1,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,3,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[3,2,1,1,1],[2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[[2,2,2,2],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,2,2,2],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[2,2,2,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[3,2,2,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[[2,2,1,1,1,1],[1,1]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[[2,1,1,1,1,1],[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[3,2,1,1,1,1],[2,1]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
>>> Load all 311 entries. <<<
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
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
inner shape
Description
The inner shape of a skew partition.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!