Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000725
Mapping
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
St000725: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1,0]
 => [1,0]
 => [1] => 1
[1,1] => [1,0,1,0]
 => [1,0,1,0]
 => [1,2] => 2
[2] => [1,1,0,0]
 => [1,1,0,0]
 => [2,1] => 2
[1,1,1] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,2,3] => 3
[1,2] => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => [2,3,1] => 3
[2,1] => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => [2,1,3] => 2
[3] => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => [3,1,2] => 2
[1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 4
[1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => 4
[1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [2,3,1,4] => 3
[1,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => 2
[2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 2
[2,2] => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => 3
[3,1] => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => 3
[4] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [4,1,2,3] => 3
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => 5
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => 5
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => 4
[1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,4,5,1,2] => 2
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => 3
[1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [3,4,1,5,2] => 4
[1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [3,4,1,2,5] => 4
[1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [4,5,1,2,3] => 3
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 2
[2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,1,4,5,2] => 3
[2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [3,1,4,2,5] => 3
[2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [4,1,5,2,3] => 3
[3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,1,2,4,5] => 3
[3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1,2,5,3] => 4
[4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [4,1,2,3,5] => 4
[5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5,1,2,3,4] => 4
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5,6] => 6
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,6,1] => 6
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [2,3,4,5,1,6] => 5
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,4,5,6,1,2] => 2
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [2,3,4,1,5,6] => 4
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [3,4,5,1,6,2] => 5
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [3,4,5,1,2,6] => 5
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [4,5,6,1,2,3] => 3
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [2,3,1,4,5,6] => 3
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [3,4,1,5,6,2] => 4
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [3,4,1,5,2,6] => 4
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => [4,5,1,6,2,3] => 3
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => [3,4,1,2,5,6] => 4
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [4,5,1,2,6,3] => 5
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [4,5,1,2,3,6] => 5
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [5,6,1,2,3,4] => 4
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,1,3,4,5,6] => 2
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [3,1,4,5,6,2] => 3
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0]
 => [3,1,4,5,2,6] => 3
Description
The smallest label of a leaf of the increasing binary tree associated to a permutation.