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Matching statistic: St000558
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Mp00221: Set partitions —conjugate⟶ Set partitions
St000558: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Mp00221: Set partitions —conjugate⟶ Set partitions
St000558: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => {{1},{2}}
=> {{1},{2}}
=> {{1,2}}
=> 1
[2,1] => {{1,2}}
=> {{1,2}}
=> {{1},{2}}
=> 0
[1,2,3] => {{1},{2},{3}}
=> {{1},{2},{3}}
=> {{1,2,3}}
=> 3
[1,3,2] => {{1},{2,3}}
=> {{1,3},{2}}
=> {{1},{2,3}}
=> 1
[2,1,3] => {{1,2},{3}}
=> {{1,2},{3}}
=> {{1,2},{3}}
=> 1
[2,3,1] => {{1,2,3}}
=> {{1,2,3}}
=> {{1},{2},{3}}
=> 0
[3,1,2] => {{1,3},{2}}
=> {{1},{2,3}}
=> {{1,3},{2}}
=> 1
[3,2,1] => {{1,3},{2}}
=> {{1},{2,3}}
=> {{1,3},{2}}
=> 1
[1,2,3,4] => {{1},{2},{3},{4}}
=> {{1},{2},{3},{4}}
=> {{1,2,3,4}}
=> 6
[1,2,4,3] => {{1},{2},{3,4}}
=> {{1,4},{2},{3}}
=> {{1},{2,3,4}}
=> 3
[1,3,2,4] => {{1},{2,3},{4}}
=> {{1,3},{2},{4}}
=> {{1,2},{3,4}}
=> 2
[1,3,4,2] => {{1},{2,3,4}}
=> {{1,3},{2,4}}
=> {{1,3},{2,4}}
=> 2
[1,4,2,3] => {{1},{2,4},{3}}
=> {{1},{2,4},{3}}
=> {{1,4},{2,3}}
=> 2
[1,4,3,2] => {{1},{2,4},{3}}
=> {{1},{2,4},{3}}
=> {{1,4},{2,3}}
=> 2
[2,1,3,4] => {{1,2},{3},{4}}
=> {{1,2},{3},{4}}
=> {{1,2,3},{4}}
=> 3
[2,1,4,3] => {{1,2},{3,4}}
=> {{1,2,4},{3}}
=> {{1},{2,3},{4}}
=> 1
[2,3,1,4] => {{1,2,3},{4}}
=> {{1,2,3},{4}}
=> {{1,2},{3},{4}}
=> 1
[2,3,4,1] => {{1,2,3,4}}
=> {{1,2,3,4}}
=> {{1},{2},{3},{4}}
=> 0
[2,4,1,3] => {{1,2,4},{3}}
=> {{1,2},{3,4}}
=> {{1,3},{2},{4}}
=> 1
[2,4,3,1] => {{1,2,4},{3}}
=> {{1,2},{3,4}}
=> {{1,3},{2},{4}}
=> 1
[3,1,2,4] => {{1,3},{2},{4}}
=> {{1},{2,3},{4}}
=> {{1,2,4},{3}}
=> 3
[3,1,4,2] => {{1,3,4},{2}}
=> {{1},{2,3,4}}
=> {{1,4},{2},{3}}
=> 1
[3,2,1,4] => {{1,3},{2},{4}}
=> {{1},{2,3},{4}}
=> {{1,2,4},{3}}
=> 3
[3,2,4,1] => {{1,3,4},{2}}
=> {{1},{2,3,4}}
=> {{1,4},{2},{3}}
=> 1
[3,4,1,2] => {{1,3},{2,4}}
=> {{1,4},{2,3}}
=> {{1},{2,4},{3}}
=> 1
[3,4,2,1] => {{1,3},{2,4}}
=> {{1,4},{2,3}}
=> {{1},{2,4},{3}}
=> 1
[4,1,2,3] => {{1,4},{2},{3}}
=> {{1},{2},{3,4}}
=> {{1,3,4},{2}}
=> 3
[4,1,3,2] => {{1,4},{2},{3}}
=> {{1},{2},{3,4}}
=> {{1,3,4},{2}}
=> 3
[4,2,1,3] => {{1,4},{2},{3}}
=> {{1},{2},{3,4}}
=> {{1,3,4},{2}}
=> 3
[4,2,3,1] => {{1,4},{2},{3}}
=> {{1},{2},{3,4}}
=> {{1,3,4},{2}}
=> 3
[4,3,1,2] => {{1,4},{2,3}}
=> {{1,3,4},{2}}
=> {{1},{2},{3,4}}
=> 1
[4,3,2,1] => {{1,4},{2,3}}
=> {{1,3,4},{2}}
=> {{1},{2},{3,4}}
=> 1
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
=> {{1},{2},{3},{4},{5}}
=> {{1,2,3,4,5}}
=> 10
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
=> {{1,5},{2},{3},{4}}
=> {{1},{2,3,4,5}}
=> 6
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
=> {{1,4},{2},{3},{5}}
=> {{1,2},{3,4,5}}
=> 4
[1,2,4,5,3] => {{1},{2},{3,4,5}}
=> {{1,4},{2,5},{3}}
=> {{1,3,4},{2,5}}
=> 4
[1,2,5,3,4] => {{1},{2},{3,5},{4}}
=> {{1},{2,5},{3},{4}}
=> {{1,5},{2,3,4}}
=> 4
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
=> {{1},{2,5},{3},{4}}
=> {{1,5},{2,3,4}}
=> 4
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
=> {{1,3},{2},{4},{5}}
=> {{1,2,3},{4,5}}
=> 4
[1,3,2,5,4] => {{1},{2,3},{4,5}}
=> {{1,3},{2,5},{4}}
=> {{1,4},{2,3,5}}
=> 4
[1,3,4,2,5] => {{1},{2,3,4},{5}}
=> {{1,3},{2,4},{5}}
=> {{1,2,4},{3,5}}
=> 4
[1,3,4,5,2] => {{1},{2,3,4,5}}
=> {{1,3,5},{2,4}}
=> {{1},{2,4},{3,5}}
=> 2
[1,3,5,2,4] => {{1},{2,3,5},{4}}
=> {{1,3,5},{2},{4}}
=> {{1},{2,3},{4,5}}
=> 2
[1,3,5,4,2] => {{1},{2,3,5},{4}}
=> {{1,3,5},{2},{4}}
=> {{1},{2,3},{4,5}}
=> 2
[1,4,2,3,5] => {{1},{2,4},{3},{5}}
=> {{1},{2,4},{3},{5}}
=> {{1,2,5},{3,4}}
=> 4
[1,4,2,5,3] => {{1},{2,4,5},{3}}
=> {{1},{2,4},{3,5}}
=> {{1,3,5},{2,4}}
=> 4
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
=> {{1},{2,4},{3},{5}}
=> {{1,2,5},{3,4}}
=> 4
[1,4,3,5,2] => {{1},{2,4,5},{3}}
=> {{1},{2,4},{3,5}}
=> {{1,3,5},{2,4}}
=> 4
[1,4,5,2,3] => {{1},{2,4},{3,5}}
=> {{1,5},{2,4},{3}}
=> {{1},{2,5},{3,4}}
=> 2
[1,4,5,3,2] => {{1},{2,4},{3,5}}
=> {{1,5},{2,4},{3}}
=> {{1},{2,5},{3,4}}
=> 2
Description
The number of occurrences of the pattern {{1,2}} in a set partition.
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