Identifier
Values
[1] => [1,0,1,0] => [3,1,2] => [1,3,2] => 2
[2] => [1,1,0,0,1,0] => [2,4,1,3] => [3,1,4,2] => 3
[1,1] => [1,0,1,1,0,0] => [3,1,4,2] => [4,2,1,3] => 2
[2,1] => [1,0,1,0,1,0] => [4,1,2,3] => [1,3,4,2] => 4
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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 Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.