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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001051
Mapping
Mp00151: Permutations —to cycle type⟶ Set partitions
St001051: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => {{1}}
 => 1
[1,2] => {{1},{2}}
 => 2
[2,1] => {{1,2}}
 => 1
[1,2,3] => {{1},{2},{3}}
 => 3
[1,3,2] => {{1},{2,3}}
 => 2
[2,1,3] => {{1,2},{3}}
 => 2
[2,3,1] => {{1,2,3}}
 => 1
[3,1,2] => {{1,2,3}}
 => 1
[3,2,1] => {{1,3},{2}}
 => 1
[1,2,3,4] => {{1},{2},{3},{4}}
 => 4
[1,2,4,3] => {{1},{2},{3,4}}
 => 2
[1,3,2,4] => {{1},{2,3},{4}}
 => 3
[1,3,4,2] => {{1},{2,3,4}}
 => 2
[1,4,2,3] => {{1},{2,3,4}}
 => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => 3
[2,1,3,4] => {{1,2},{3},{4}}
 => 3
[2,1,4,3] => {{1,2},{3,4}}
 => 2
[2,3,1,4] => {{1,2,3},{4}}
 => 2
[2,3,4,1] => {{1,2,3,4}}
 => 1
[2,4,1,3] => {{1,2,3,4}}
 => 1
[2,4,3,1] => {{1,2,4},{3}}
 => 1
[3,1,2,4] => {{1,2,3},{4}}
 => 2
[3,1,4,2] => {{1,2,3,4}}
 => 1
[3,2,1,4] => {{1,3},{2},{4}}
 => 2
[3,2,4,1] => {{1,3,4},{2}}
 => 1
[3,4,1,2] => {{1,3},{2,4}}
 => 2
[3,4,2,1] => {{1,2,3,4}}
 => 1
[4,1,2,3] => {{1,2,3,4}}
 => 1
[4,1,3,2] => {{1,2,4},{3}}
 => 1
[4,2,1,3] => {{1,3,4},{2}}
 => 1
[4,2,3,1] => {{1,4},{2},{3}}
 => 1
[4,3,1,2] => {{1,2,3,4}}
 => 1
[4,3,2,1] => {{1,4},{2,3}}
 => 1
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => 5
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => 3
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => 3
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => 2
[1,2,5,3,4] => {{1},{2},{3,4,5}}
 => 2
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => 2
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => 4
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => 2
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => 3
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => 2
[1,3,5,2,4] => {{1},{2,3,4,5}}
 => 2
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => 3
[1,4,2,3,5] => {{1},{2,3,4},{5}}
 => 3
[1,4,2,5,3] => {{1},{2,3,4,5}}
 => 2
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => 4
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => 2
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => 3
Description
The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. The bijection between set partitions of {1,…,n} into k blocks and trees with n+1−k leaves is described in Theorem 1 of [1].