Identifier
Values
[1] => [1,0,1,0] => [1,1,0,1,0,0] => [2,3,1] => 1
[2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 1
[1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => 1
[2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 3
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searching the database for statistics with the same generating function
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.