Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001584
Mapping
Mp00053: Parking functions —to car permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001584: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1] => [1,0]
 => 0
[1,1] => [1,2] => [1,2] => [1,0,1,0]
 => 0
[1,2] => [1,2] => [1,2] => [1,0,1,0]
 => 0
[2,1] => [2,1] => [2,1] => [1,1,0,0]
 => 0
[1,1,1] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 0
[1,1,2] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 0
[1,2,1] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 0
[2,1,1] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 0
[1,1,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 0
[1,3,1] => [1,3,2] => [2,3,1] => [1,1,0,1,0,0]
 => 1
[3,1,1] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
 => 0
[1,2,2] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 0
[2,1,2] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 0
[2,2,1] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0]
 => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 0
[1,3,2] => [1,3,2] => [2,3,1] => [1,1,0,1,0,0]
 => 1
[2,1,3] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 0
[2,3,1] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0]
 => 0
[3,1,2] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
 => 0
[3,2,1] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
 => 0
[1,1,1,1] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,1,1,2] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,1,2,1] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,2,1,1] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[2,1,1,1] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 0
[1,1,1,3] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,1,3,1] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,3,1,1] => [1,3,2,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
 => 1
[3,1,1,1] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
 => 0
[1,1,1,4] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,1,4,1] => [1,2,4,3] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
 => 1
[1,4,1,1] => [1,3,4,2] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
 => 1
[4,1,1,1] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
 => 0
[1,1,2,2] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,2,1,2] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,2,2,1] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[2,1,1,2] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 0
[2,1,2,1] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 0
[2,2,1,1] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 0
[1,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,1,3,2] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,2,1,3] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
[1,3,1,2] => [1,3,2,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
 => 1
[1,3,2,1] => [1,3,2,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
 => 1
[2,1,1,3] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 0
[2,1,3,1] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 0
[2,3,1,1] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 0
[3,1,1,2] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
 => 0
[3,1,2,1] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
 => 0
Description
The area statistic between a Dyck path and its bounce path. The bounce path [[Mp00099]] is weakly below a given Dyck path and this statistic records the number of boxes between the two paths.
Matching statistic: St001857
Mapping
Mp00053: Parking functions —to car permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 29%
Values
[1] => [1] => [1] => [1] => 0
[1,1] => [1,2] => [2,1] => [2,1] => 0
[1,2] => [1,2] => [2,1] => [2,1] => 0
[2,1] => [2,1] => [1,2] => [1,2] => 0
[1,1,1] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,1,2] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,2,1] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[2,1,1] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[1,1,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,3,1] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[3,1,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,2,2] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[2,1,2] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,2,1] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[2,1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,3,1] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[3,1,2] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[1,1,1,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,1,1,2] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,1,2,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,1,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[2,1,1,1] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => ? = 0
[1,1,1,3] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,1,3,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,3,1,1] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[3,1,1,1] => [2,3,1,4] => [1,2,4,3] => [1,2,4,3] => ? = 0
[1,1,1,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,1,4,1] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,4,1,1] => [1,3,4,2] => [4,2,3,1] => [4,2,3,1] => ? = 1
[4,1,1,1] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => ? = 0
[1,1,2,2] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,1,2] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,2,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[2,1,1,2] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => ? = 0
[2,1,2,1] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => ? = 0
[2,2,1,1] => [3,1,2,4] => [3,1,4,2] => [3,1,4,2] => ? = 0
[1,1,2,3] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,1,3,2] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,1,3] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,3,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,3,1,2] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,3,2,1] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[2,1,1,3] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => ? = 0
[2,1,3,1] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => ? = 0
[2,3,1,1] => [3,1,2,4] => [3,1,4,2] => [3,1,4,2] => ? = 0
[3,1,1,2] => [2,3,1,4] => [1,2,4,3] => [1,2,4,3] => ? = 0
[3,1,2,1] => [2,3,1,4] => [1,2,4,3] => [1,2,4,3] => ? = 0
[3,2,1,1] => [3,2,1,4] => [2,1,4,3] => [2,1,4,3] => ? = 0
[1,1,2,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,1,4,2] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,2,1,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,4,1] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,4,1,2] => [1,3,4,2] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,4,2,1] => [1,3,4,2] => [4,2,3,1] => [4,2,3,1] => ? = 1
[2,1,1,4] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => ? = 0
[2,1,4,1] => [2,1,4,3] => [1,4,3,2] => [1,4,3,2] => ? = 2
[2,4,1,1] => [3,1,4,2] => [4,1,3,2] => [4,1,3,2] => ? = 2
[4,1,1,2] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => ? = 0
[4,1,2,1] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => ? = 0
[4,2,1,1] => [3,2,4,1] => [2,1,3,4] => [2,1,3,4] => ? = 0
[1,1,3,3] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,3,1,3] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,3,3,1] => [1,4,2,3] => [3,4,2,1] => [3,4,2,1] => ? = 0
[3,1,1,3] => [2,3,1,4] => [1,2,4,3] => [1,2,4,3] => ? = 0
[3,1,3,1] => [2,4,1,3] => [1,4,2,3] => [1,4,2,3] => ? = 1
[3,3,1,1] => [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => ? = 0
[1,1,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
Description
The number of edges in the reduced word graph of a signed permutation. The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.