Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000308
Mapping
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
St000308: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1] => [1] => [1] => 1
[1,0,1,0]
 => [1,2] => [1,2] => [1,2] => 2
[1,1,0,0]
 => [2,1] => [2,1] => [2,1] => 1
[1,0,1,0,1,0]
 => [1,2,3] => [1,2,3] => [1,2,3] => 3
[1,0,1,1,0,0]
 => [1,3,2] => [3,1,2] => [1,3,2] => 2
[1,1,0,0,1,0]
 => [2,1,3] => [2,1,3] => [2,1,3] => 2
[1,1,0,1,0,0]
 => [2,3,1] => [3,2,1] => [3,2,1] => 1
[1,1,1,0,0,0]
 => [3,2,1] => [2,3,1] => [2,3,1] => 2
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [3,1,2,4] => [1,3,2,4] => 3
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => [3,1,4,2] => [3,4,1,2] => 2
[1,0,1,1,1,0,0,0]
 => [1,4,3,2] => [4,1,3,2] => [4,1,3,2] => 2
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [2,1,4,3] => [4,2,1,3] => 2
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 2
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [3,2,4,1] => [3,2,4,1] => 2
[1,1,0,1,1,0,0,0]
 => [2,4,3,1] => [4,2,3,1] => [2,4,3,1] => 2
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [2,3,1,4] => [2,3,1,4] => 2
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => [2,3,4,1] => [2,3,4,1] => 3
[1,1,1,0,1,0,0,0]
 => [3,4,2,1] => [4,3,2,1] => [4,3,2,1] => 1
[1,1,1,1,0,0,0,0]
 => [4,3,2,1] => [3,4,2,1] => [3,4,2,1] => 2
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 5
[1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => [1,2,5,3,4] => [1,5,2,3,4] => 4
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [1,2,4,3,5] => [4,1,2,3,5] => 4
[1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => [1,2,5,4,3] => [5,4,1,2,3] => 3
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => [1,2,4,5,3] => [4,1,2,5,3] => 3
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [3,1,2,4,5] => [1,3,2,4,5] => 4
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [3,1,2,5,4] => [5,1,3,2,4] => 3
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => 3
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => [3,1,4,5,2] => [3,4,1,5,2] => 2
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => [3,1,5,4,2] => [5,3,4,1,2] => 2
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [4,1,3,2,5] => [4,1,3,2,5] => 3
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [4,1,3,5,2] => [4,1,3,5,2] => 3
[1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,3,2] => [4,1,5,3,2] => [4,5,3,1,2] => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => [5,1,4,3,2] => [5,4,1,3,2] => 2
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 4
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [2,1,5,3,4] => [2,5,1,3,4] => 3
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [2,1,4,3,5] => [4,2,1,3,5] => 3
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [2,1,5,4,3] => [5,4,2,1,3] => 2
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [2,1,4,5,3] => [4,2,1,5,3] => 2
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 3
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [3,2,1,5,4] => [5,3,2,1,4] => 2
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [3,2,4,1,5] => [3,2,4,1,5] => 2
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [3,2,4,5,1] => [3,2,4,5,1] => 3
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => [3,2,5,4,1] => [5,3,2,4,1] => 2
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [4,2,3,1,5] => [2,4,3,1,5] => 2
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [4,2,3,5,1] => [2,4,3,5,1] => 3
[1,1,0,1,1,0,1,0,0,0]
 => [2,4,5,3,1] => [4,2,5,3,1] => [4,5,2,3,1] => 2
[1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => [5,2,4,3,1] => [5,2,4,3,1] => 2
Description
The height of the tree associated to a permutation. A permutation can be mapped to a rooted tree with vertices $\{0,1,2,\ldots,n\}$ and root $0$ in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1]. The statistic is given by the height of this tree. See also [[St000325]] for the width of this tree.