Identifier
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Mp00199:
Dyck paths
—prime Dyck path⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001583: Permutations ⟶ ℤ (values match St000246The number of non-inversions of a permutation.)
Values
[1,0] => [1,1,0,0] => [2,3,1] => 1
[1,0,1,0] => [1,1,0,1,0,0] => [4,3,1,2] => 1
[1,1,0,0] => [1,1,1,0,0,0] => [2,3,4,1] => 3
[] => [1,0] => [2,1] => 0
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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
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
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