Identifier
-
Mp00043:
Integer partitions
—to Dyck path⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St001583: Permutations ⟶ ℤ (values match St000246The number of non-inversions of a permutation.)
Values
[1] => [1,0,1,0] => [3,1,2] => [1,3,2] => 2
[2] => [1,1,0,0,1,0] => [2,4,1,3] => [2,4,1,3] => 3
[1,1] => [1,0,1,1,0,0] => [3,1,4,2] => [3,1,4,2] => 3
[2,1] => [1,0,1,0,1,0] => [4,1,2,3] => [1,2,4,3] => 5
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Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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