Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤ
Values
[1,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[2,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[1,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[3,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[2,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[2,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[4,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[3,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[3,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[2,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[5,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[4,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[4,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[3,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[6,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[5,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[5,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[4,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[7,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[6,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[6,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[5,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[8,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[7,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[7,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[6,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[9,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[8,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[8,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[7,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[10,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[9,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[9,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[8,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[11,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[10,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[10,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[9,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[12,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[11,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[11,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[10,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[13,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[12,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[12,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[11,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[14,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[13,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[13,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[12,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[15,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[14,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[14,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[13,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
[16,1] => [1] => [1,0,1,0] => [3,1,2] => 1
[15,2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[15,1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[14,2,1] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
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Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Map
first row removal
Description
Removes the first entry of an integer partition
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.
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