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Matching statistic: St001898
Mapping
St001898: Ordered set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[{1}] => 0
[{1},{2}] => 0
[{2},{1}] => 0
[{1,2}] => 0
[{1},{2},{3}] => 0
[{1},{3},{2}] => 1
[{2},{1},{3}] => 0
[{3},{1},{2}] => 0
[{2},{3},{1}] => 0
[{3},{2},{1}] => 0
[{1},{2,3}] => 0
[{2},{1,3}] => 0
[{3},{1,2}] => 0
[{1,2},{3}] => 0
[{1,3},{2}] => 0
[{2,3},{1}] => 0
[{1,2,3}] => 0
[{1},{2},{3},{4}] => 0
[{1},{2},{4},{3}] => 2
[{1},{3},{2},{4}] => 1
[{1},{4},{2},{3}] => 2
[{1},{3},{4},{2}] => 2
[{1},{4},{3},{2}] => 3
[{2},{1},{3},{4}] => 0
[{2},{1},{4},{3}] => 2
[{3},{1},{2},{4}] => 0
[{4},{1},{2},{3}] => 0
[{3},{1},{4},{2}] => 1
[{4},{1},{3},{2}] => 1
[{2},{3},{1},{4}] => 0
[{2},{4},{1},{3}] => 1
[{3},{2},{1},{4}] => 0
[{4},{2},{1},{3}] => 0
[{3},{4},{1},{2}] => 0
[{4},{3},{1},{2}] => 0
[{2},{3},{4},{1}] => 0
[{2},{4},{3},{1}] => 1
[{3},{2},{4},{1}] => 0
[{4},{2},{3},{1}] => 0
[{3},{4},{2},{1}] => 0
[{4},{3},{2},{1}] => 0
[{1},{2},{3,4}] => 0
[{1},{3},{2,4}] => 1
[{1},{4},{2,3}] => 2
[{2},{1},{3,4}] => 0
[{3},{1},{2,4}] => 0
[{4},{1},{2,3}] => 0
[{2},{3},{1,4}] => 0
[{2},{4},{1,3}] => 1
[{3},{2},{1,4}] => 0
Description
The number of occurrences of an 132 pattern in an ordered set partition. An occurrence of a pattern $\pi\in\mathfrak S_k$ ordered set partition with blocks $B_1|\dots|B_\ell$ is a sequence of elements $e_1,\dots,e_k$ with $e_i\in B_{j_i}$ and $j_1 < \dots < j_k$ order-isomorphic to $\pi$.