Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001153
Mapping
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St001153: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1,0]
 => {{1}}
 => 0
[1,1] => [2] => [1,1,0,0]
 => {{1,2}}
 => 0
[2] => [1] => [1,0]
 => {{1}}
 => 0
[1,1,1] => [3] => [1,1,1,0,0,0]
 => {{1,2,3}}
 => 0
[1,2] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[2,1] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[3] => [1] => [1,0]
 => {{1}}
 => 0
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
 => {{1,2,3,4}}
 => 0
[1,1,2] => [2,1] => [1,1,0,0,1,0]
 => {{1,2},{3}}
 => 0
[1,2,1] => [1,1,1] => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 1
[1,3] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[2,1,1] => [1,2] => [1,0,1,1,0,0]
 => {{1},{2,3}}
 => 1
[2,2] => [2] => [1,1,0,0]
 => {{1,2}}
 => 0
[3,1] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[4] => [1] => [1,0]
 => {{1}}
 => 0
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
 => {{1,2,3,4,5}}
 => 0
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
 => {{1,2,3},{4}}
 => 1
[1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => {{1,2},{3},{4}}
 => 1
[1,1,3] => [2,1] => [1,1,0,0,1,0]
 => {{1,2},{3}}
 => 0
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => {{1},{2},{3,4}}
 => 1
[1,2,2] => [1,2] => [1,0,1,1,0,0]
 => {{1},{2,3}}
 => 1
[1,3,1] => [1,1,1] => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 1
[1,4] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
 => {{1},{2,3,4}}
 => 1
[2,1,2] => [1,1,1] => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 1
[2,2,1] => [2,1] => [1,1,0,0,1,0]
 => {{1,2},{3}}
 => 0
[2,3] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[3,1,1] => [1,2] => [1,0,1,1,0,0]
 => {{1},{2,3}}
 => 1
[3,2] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[4,1] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[5] => [1] => [1,0]
 => {{1}}
 => 0
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => {{1,2,3,4,5,6}}
 => 0
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => {{1,2,3,4},{5}}
 => 0
[1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => {{1,2,3},{4},{5}}
 => 1
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
 => {{1,2,3},{4}}
 => 1
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => {{1,2},{3},{4,5}}
 => 1
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => {{1,2},{3,4}}
 => 0
[1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => {{1,2},{3},{4}}
 => 1
[1,1,4] => [2,1] => [1,1,0,0,1,0]
 => {{1,2},{3}}
 => 0
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => {{1},{2},{3,4,5}}
 => 1
[1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => {{1},{2},{3},{4}}
 => 2
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => {{1},{2,3},{4}}
 => 2
[1,2,3] => [1,1,1] => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 1
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => {{1},{2},{3,4}}
 => 1
[1,3,2] => [1,1,1] => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 1
[1,4,1] => [1,1,1] => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 1
[1,5] => [1,1] => [1,0,1,0]
 => {{1},{2}}
 => 1
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => {{1},{2,3,4,5}}
 => 1
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => {{1},{2,3},{4}}
 => 2
[2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => {{1},{2},{3},{4}}
 => 2
Description
The number of blocks with even minimum in a set partition.