Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001191
Mapping
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001191: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1] => [1] => [1,0]
 => 1
[1,0,1,0]
 => [1,2] => [1,2] => [1,0,1,0]
 => 1
[1,1,0,0]
 => [2,1] => [2,1] => [1,1,0,0]
 => 2
[1,0,1,0,1,0]
 => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 1
[1,0,1,1,0,0]
 => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 1
[1,1,0,0,1,0]
 => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 1
[1,1,0,1,0,0]
 => [2,3,1] => [3,2,1] => [1,1,1,0,0,0]
 => 3
[1,1,1,0,0,0]
 => [3,2,1] => [2,3,1] => [1,1,0,1,0,0]
 => 1
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 1
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 2
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 1
[1,0,1,1,1,0,0,0]
 => [1,4,3,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => 0
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 1
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
 => 1
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => 1
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => 4
[1,1,0,1,1,0,0,0]
 => [2,4,3,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
 => 1
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
 => 1
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
 => 1
[1,1,1,0,1,0,0,0]
 => [4,2,3,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
 => 1
[1,1,1,1,0,0,0,0]
 => [4,3,2,1] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => 0
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => 2
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => 2
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => 2
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => 0
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => 0
[1,0,1,1,1,0,1,0,0,0]
 => [1,5,3,4,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => 0
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => 1
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => 2
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
 => 0
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => 1
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
 => 1
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => 5
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0]
 => 1
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
 => 1
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
 => 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,5,3,4,1] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
 => 1
[1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
 => 1
Description
Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$.