Identifier
-
Mp00201:
Dyck paths
—Ringel⟶
Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00244: Signed permutations —bar⟶ Signed permutations
St001773: Signed permutations ⟶ ℤ
Values
[1,0] => [2,1] => [2,1] => [-2,-1] => 1
[1,0,1,0] => [3,1,2] => [3,1,2] => [-3,-1,-2] => 1
[1,1,0,0] => [2,3,1] => [2,3,1] => [-2,-3,-1] => 1
[1,0,1,0,1,0] => [4,1,2,3] => [4,1,2,3] => [-4,-1,-2,-3] => 1
[1,0,1,1,0,0] => [3,1,4,2] => [3,1,4,2] => [-3,-1,-4,-2] => 2
[1,1,0,0,1,0] => [2,4,1,3] => [2,4,1,3] => [-2,-4,-1,-3] => 2
[1,1,0,1,0,0] => [4,3,1,2] => [4,3,1,2] => [-4,-3,-1,-2] => 2
[1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => [-2,-3,-4,-1] => 1
[] => [1] => [1] => [-1] => 0
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Description
The number of minimal elements in Bruhat order not less than the signed permutation.
The minimal elements in question are biGrassmannian, that is both the element and its inverse have at most one descent.
This is the size of the essential set of the signed permutation, see [1].
The minimal elements in question are biGrassmannian, that is both the element and its inverse have at most one descent.
This is the size of the essential set of the signed permutation, see [1].
Map
bar
Description
Return the signed permutation with all signs reversed.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
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