Identifier
Values
([2],3) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 3
([1,1],3) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 3
([3,1],3) => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
([2],4) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 3
([1,1],4) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 3
([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] => 3
([1,1],5) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 3
([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] => 3
([1,1],6) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 3
([2,1],6) => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
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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
to bounded partition
Description
The (k-1)-bounded partition of a k-core.
Starting with a $k$-core, deleting all cells of hook length greater than or equal to $k$ yields a $(k-1)$-bounded partition [1, Theorem 7], see also [2, Section 1.2].
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.