Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000554
(load all 2 compositions to match this statistic)
Mapping
St000554: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => 0
{{1},{2}}
 => 0
{{1,2,3}}
 => 0
{{1,2},{3}}
 => 1
{{1,3},{2}}
 => 0
{{1},{2,3}}
 => 0
{{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => 3
{{1,2,4},{3}}
 => 1
{{1,2},{3,4}}
 => 2
{{1,2},{3},{4}}
 => 2
{{1,3,4},{2}}
 => 0
{{1,3},{2,4}}
 => 1
{{1,3},{2},{4}}
 => 1
{{1,4},{2,3}}
 => 1
{{1},{2,3,4}}
 => 0
{{1},{2,3},{4}}
 => 1
{{1,4},{2},{3}}
 => 0
{{1},{2,4},{3}}
 => 0
{{1},{2},{3,4}}
 => 0
{{1},{2},{3},{4}}
 => 0
{{1,2,3,4,5}}
 => 0
{{1,2,3,4},{5}}
 => 6
{{1,2,3,5},{4}}
 => 3
{{1,2,3},{4,5}}
 => 6
{{1,2,3},{4},{5}}
 => 6
{{1,2,4,5},{3}}
 => 1
{{1,2,4},{3,5}}
 => 4
{{1,2,4},{3},{5}}
 => 4
{{1,2,5},{3,4}}
 => 3
{{1,2},{3,4,5}}
 => 3
{{1,2},{3,4},{5}}
 => 4
{{1,2,5},{3},{4}}
 => 2
{{1,2},{3,5},{4}}
 => 3
{{1,2},{3},{4,5}}
 => 3
{{1,2},{3},{4},{5}}
 => 3
{{1,3,4,5},{2}}
 => 0
{{1,3,4},{2,5}}
 => 3
{{1,3,4},{2},{5}}
 => 3
{{1,3,5},{2,4}}
 => 2
{{1,3},{2,4,5}}
 => 2
{{1,3},{2,4},{5}}
 => 3
{{1,3,5},{2},{4}}
 => 1
{{1,3},{2,5},{4}}
 => 2
{{1,3},{2},{4,5}}
 => 2
{{1,3},{2},{4},{5}}
 => 2
{{1,4,5},{2,3}}
 => 2
{{1,4},{2,3,5}}
 => 2
{{1,4},{2,3},{5}}
 => 3
Description
The number of occurrences of the pattern {{1,2},{3}} in a set partition.
Matching statistic: St000556
Mapping
Mp00112: Set partitions —complement⟶ Set partitions
St000556: Set partitions ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => {{1,2}}
 => 0
{{1},{2}}
 => {{1},{2}}
 => 0
{{1,2,3}}
 => {{1,2,3}}
 => 0
{{1,2},{3}}
 => {{1},{2,3}}
 => 1
{{1,3},{2}}
 => {{1,3},{2}}
 => 0
{{1},{2,3}}
 => {{1,2},{3}}
 => 0
{{1},{2},{3}}
 => {{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => {{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => {{1},{2,3,4}}
 => 3
{{1,2,4},{3}}
 => {{1,3,4},{2}}
 => 1
{{1,2},{3,4}}
 => {{1,2},{3,4}}
 => 2
{{1,2},{3},{4}}
 => {{1},{2},{3,4}}
 => 2
{{1,3,4},{2}}
 => {{1,2,4},{3}}
 => 0
{{1,3},{2,4}}
 => {{1,3},{2,4}}
 => 1
{{1,3},{2},{4}}
 => {{1},{2,4},{3}}
 => 1
{{1,4},{2,3}}
 => {{1,4},{2,3}}
 => 1
{{1},{2,3,4}}
 => {{1,2,3},{4}}
 => 0
{{1},{2,3},{4}}
 => {{1},{2,3},{4}}
 => 1
{{1,4},{2},{3}}
 => {{1,4},{2},{3}}
 => 0
{{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => 0
{{1},{2},{3,4}}
 => {{1,2},{3},{4}}
 => 0
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => 0
{{1,2,3,4,5}}
 => {{1,2,3,4,5}}
 => 0
{{1,2,3,4},{5}}
 => {{1},{2,3,4,5}}
 => 6
{{1,2,3,5},{4}}
 => {{1,3,4,5},{2}}
 => 3
{{1,2,3},{4,5}}
 => {{1,2},{3,4,5}}
 => 6
{{1,2,3},{4},{5}}
 => {{1},{2},{3,4,5}}
 => 6
{{1,2,4,5},{3}}
 => {{1,2,4,5},{3}}
 => 1
{{1,2,4},{3,5}}
 => {{1,3},{2,4,5}}
 => 4
{{1,2,4},{3},{5}}
 => {{1},{2,4,5},{3}}
 => 4
{{1,2,5},{3,4}}
 => {{1,4,5},{2,3}}
 => 3
{{1,2},{3,4,5}}
 => {{1,2,3},{4,5}}
 => 3
{{1,2},{3,4},{5}}
 => {{1},{2,3},{4,5}}
 => 4
{{1,2,5},{3},{4}}
 => {{1,4,5},{2},{3}}
 => 2
{{1,2},{3,5},{4}}
 => {{1,3},{2},{4,5}}
 => 3
{{1,2},{3},{4,5}}
 => {{1,2},{3},{4,5}}
 => 3
{{1,2},{3},{4},{5}}
 => {{1},{2},{3},{4,5}}
 => 3
{{1,3,4,5},{2}}
 => {{1,2,3,5},{4}}
 => 0
{{1,3,4},{2,5}}
 => {{1,4},{2,3,5}}
 => 3
{{1,3,4},{2},{5}}
 => {{1},{2,3,5},{4}}
 => 3
{{1,3,5},{2,4}}
 => {{1,3,5},{2,4}}
 => 2
{{1,3},{2,4,5}}
 => {{1,2,4},{3,5}}
 => 2
{{1,3},{2,4},{5}}
 => {{1},{2,4},{3,5}}
 => 3
{{1,3,5},{2},{4}}
 => {{1,3,5},{2},{4}}
 => 1
{{1,3},{2,5},{4}}
 => {{1,4},{2},{3,5}}
 => 2
{{1,3},{2},{4,5}}
 => {{1,2},{3,5},{4}}
 => 2
{{1,3},{2},{4},{5}}
 => {{1},{2},{3,5},{4}}
 => 2
{{1,4,5},{2,3}}
 => {{1,2,5},{3,4}}
 => 2
{{1,4},{2,3,5}}
 => {{1,3,4},{2,5}}
 => 2
{{1,4},{2,3},{5}}
 => {{1},{2,5},{3,4}}
 => 3
{{1},{2},{3,4,5,6,7,8}}
 => {{1,2,3,4,5,6},{7},{8}}
 => ? = 0
{{1},{2,4,5,6,7,8},{3}}
 => {{1,2,3,4,5,7},{6},{8}}
 => ? = 0
{{1},{2,3,5,6,7,8},{4}}
 => {{1,2,3,4,6,7},{5},{8}}
 => ? = 1
{{1},{2,3,4,6,7,8},{5}}
 => {{1,2,3,5,6,7},{4},{8}}
 => ? = 3
{{1},{2,3,4,5,7,8},{6}}
 => {{1,2,4,5,6,7},{3},{8}}
 => ? = 6
{{1},{2,3,4,5,6,8},{7}}
 => {{1,3,4,5,6,7},{2},{8}}
 => ? = 10
{{1,4,5,6,7,8},{2},{3}}
 => {{1,2,3,4,5,8},{6},{7}}
 => ? = 0
{{1,3,5,6,7,8},{2},{4}}
 => {{1,2,3,4,6,8},{5},{7}}
 => ? = 1
Description
The number of occurrences of the pattern {{1},{2,3}} in a set partition.