Identifier
Values
([2],3) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
([1,1],3) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
([2],4) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
([1,1],4) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
([2,1],4) => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
([2],5) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
([1,1],5) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
([2,1],5) => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
([2],6) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
([1,1],6) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
([2,1],6) => [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 Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
to partition
Description
Considers a core as a partition.
This embedding is graded and injective but not surjective on $k$-cores for a given parameter $k$, while it is surjective and neither graded nor injective on the collection of all cores.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.