Identifier
-
Mp00037:
Graphs
—to partition of connected components⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤ
Values
([],1) => [1] => [1,0,1,0] => [3,1,2] => 1
([],2) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
([(0,1)],2) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
([(1,2)],3) => [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
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
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.
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