Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000119
Mapping
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St000119: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1,0]
 => [1] => 0
{{1,2}}
 => [2] => [1,1,0,0]
 => [2,1] => 0
{{1},{2}}
 => [1,1] => [1,0,1,0]
 => [1,2] => 0
{{1,2,3}}
 => [3] => [1,1,1,0,0,0]
 => [3,2,1] => 1
{{1,2},{3}}
 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 0
{{1,3},{2}}
 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 0
{{1},{2,3}}
 => [1,2] => [1,0,1,1,0,0]
 => [1,3,2] => 0
{{1},{2},{3}}
 => [1,1,1] => [1,0,1,0,1,0]
 => [1,2,3] => 0
{{1,2,3,4}}
 => [4] => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 4
{{1,2,3},{4}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,2,4},{3}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,2},{3,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1,2},{3},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1,3,4},{2}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,3},{2,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1,3},{2},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1,4},{2,3}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1},{2,3,4}}
 => [1,3] => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 1
{{1},{2,3},{4}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
{{1,4},{2},{3}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1},{2,4},{3}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
{{1},{2},{3,4}}
 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 0
{{1},{2},{3},{4}}
 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => 10
{{1,2,3,4},{5}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,3,5},{4}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,3},{4,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2,3},{4},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2,4,5},{3}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,4},{3,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2,4},{3},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2,5},{3,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2},{3,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,2},{3,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2,5},{3},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2},{3,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2},{3},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 0
{{1,2},{3},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 0
{{1,3,4,5},{2}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,3,4},{2,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,3,4},{2},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,3,5},{2,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,3},{2,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,3},{2,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,3,5},{2},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,3},{2,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,3},{2},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 0
{{1,3},{2},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 0
{{1,4,5},{2,3}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,4},{2,3,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
Description
The number of occurrences of the pattern 321 in a permutation.
Matching statistic: St000002
(load all 2 compositions to match this statistic)
Mapping
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000002: Permutations ⟶ ℤResult quality: 94% ●values known / values provided: 94%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1,0]
 => [1] => 0
{{1,2}}
 => [2] => [1,1,0,0]
 => [1,2] => 0
{{1},{2}}
 => [1,1] => [1,0,1,0]
 => [2,1] => 0
{{1,2,3}}
 => [3] => [1,1,1,0,0,0]
 => [1,2,3] => 1
{{1,2},{3}}
 => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 0
{{1,3},{2}}
 => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 0
{{1},{2,3}}
 => [1,2] => [1,0,1,1,0,0]
 => [2,3,1] => 0
{{1},{2},{3}}
 => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 0
{{1,2,3,4}}
 => [4] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 4
{{1,2,3},{4}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,2,4},{3}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,2},{3,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1,2},{3},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1,3,4},{2}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,3},{2,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1,3},{2},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1,4},{2,3}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1},{2,3,4}}
 => [1,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 1
{{1},{2,3},{4}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 0
{{1,4},{2},{3}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1},{2,4},{3}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 0
{{1},{2},{3,4}}
 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 0
{{1},{2},{3},{4}}
 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 0
{{1,2,3,4,5}}
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => 10
{{1,2,3,4},{5}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,3,5},{4}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,3},{4,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2,3},{4},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2,4,5},{3}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,4},{3,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2,4},{3},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2,5},{3,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2},{3,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1,2},{3,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,2,5},{3},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2},{3,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,2},{3},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 0
{{1,2},{3},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 0
{{1,3,4,5},{2}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,3,4},{2,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,3,4},{2},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,3,5},{2,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,3},{2,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1,3},{2,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,3,5},{2},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,3},{2,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,3},{2},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 0
{{1,3},{2},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 0
{{1,4,5},{2,3}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,4},{2,3,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1},{2,3},{4},{5},{6},{7}}
 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,2,3,1] => ? = 0
{{1},{2,4},{3},{5},{6},{7}}
 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,2,3,1] => ? = 0
{{1},{2,5},{3},{4},{6},{7}}
 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,2,3,1] => ? = 0
{{1},{2,6},{3},{4},{5},{7}}
 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,2,3,1] => ? = 0
{{1},{2},{3},{4},{5,6},{7}}
 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [7,5,6,4,3,2,1] => ? = 0
{{1},{2,7},{3},{4},{5},{6}}
 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,2,3,1] => ? = 0
{{1},{2},{3},{4},{5,7},{6}}
 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [7,5,6,4,3,2,1] => ? = 0
{{1},{2},{3},{4},{5},{6,7}}
 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [6,7,5,4,3,2,1] => ? = 0
{{1},{2},{3},{4},{5},{6},{7,8}}
 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [7,8,6,5,4,3,2,1] => ? = 0
{{1},{2},{3},{4},{5},{6,8},{7}}
 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [8,6,7,5,4,3,2,1] => ? = 0
{{1},{2},{3},{4,8},{5},{6},{7}}
 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [8,7,6,4,5,3,2,1] => ? = 0
{{1},{2,3},{4,5},{6,7},{8}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,3},{4,5},{6,8},{7}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,3},{4,7},{5,6},{8}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,3},{4,8},{5,6},{7}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,3},{4,8},{5,7},{6}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,8},{3},{4},{5},{6},{7}}
 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [8,7,6,5,4,2,3,1] => ? = 0
{{1},{2,5},{3,4},{6,7},{8}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,5},{3,4},{6,8},{7}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,7},{3,4},{5,6},{8}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,8},{3,4},{5,6},{7}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,8},{3,4},{5,7},{6}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,7},{3,6},{4,5},{8}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,8},{3,6},{4,5},{7}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,8},{3,7},{4,5},{6}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,8},{3,7},{4,6},{5}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1,2,3},{4,5,6,7,8}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1,7,8},{2,3,4,5,6}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1,2,8},{3,4,5,6,7}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1},{2},{3},{4},{5},{6},{7},{8,9}}
 => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [8,9,7,6,5,4,3,2,1] => ? = 0
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
 => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [9,10,8,7,6,5,4,3,2,1] => ? = 0
{{1,5,6},{2,3,4,7,8}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1},{2,6},{3,7},{4,8},{5}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,4},{3,5},{6,7},{8}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,5},{3,6},{4,7},{8}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,4},{3,6},{5,8},{7}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,6},{3,5},{4,8},{7}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,8},{3,5},{4,7},{6}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1},{2,4},{3,8},{5,7},{6}}
 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [8,6,7,4,5,2,3,1] => ? = 0
{{1,2},{3,4,5,6,7,8,9,10}}
 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [3,4,5,6,7,8,9,10,1,2] => ? = 56
{{1,2,3,4},{5,6,7,8,9,10}}
 => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [5,6,7,8,9,10,1,2,3,4] => ? = 24
{{1,10},{2,3,4,5,6,7,8,9}}
 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [3,4,5,6,7,8,9,10,1,2] => ? = 56
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
 => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [10,11,9,8,7,6,5,4,3,2,1] => ? = 0
{{1,4,6},{2,3,5,7,8}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1,2,6},{3,4,5,7,8}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1,4,7},{2,3,5,6,8}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1,2,4},{3,5,6,7,8}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1,5,8},{2,3,4,6,7}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1,3,4},{2,5,6,7,8}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
{{1,2,5},{3,4,6,7,8}}
 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [4,5,6,7,8,1,2,3] => ? = 11
Description
The number of occurrences of the pattern 123 in a permutation.
Matching statistic: St000561
(load all 33 compositions to match this statistic)
Mapping
Mp00112: Set partitions —complement⟶ Set partitions
St000561: Set partitions ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 62%
Values
{{1}}
 => {{1}}
 => ? = 0
{{1,2}}
 => {{1,2}}
 => 0
{{1},{2}}
 => {{1},{2}}
 => 0
{{1,2,3}}
 => {{1,2,3}}
 => 1
{{1,2},{3}}
 => {{1},{2,3}}
 => 0
{{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}}
 => 4
{{1,2,3},{4}}
 => {{1},{2,3,4}}
 => 1
{{1,2,4},{3}}
 => {{1,3,4},{2}}
 => 1
{{1,2},{3,4}}
 => {{1,2},{3,4}}
 => 0
{{1,2},{3},{4}}
 => {{1},{2},{3,4}}
 => 0
{{1,3,4},{2}}
 => {{1,2,4},{3}}
 => 1
{{1,3},{2,4}}
 => {{1,3},{2,4}}
 => 0
{{1,3},{2},{4}}
 => {{1},{2,4},{3}}
 => 0
{{1,4},{2,3}}
 => {{1,4},{2,3}}
 => 0
{{1},{2,3,4}}
 => {{1,2,3},{4}}
 => 1
{{1},{2,3},{4}}
 => {{1},{2,3},{4}}
 => 0
{{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}}
 => 10
{{1,2,3,4},{5}}
 => {{1},{2,3,4,5}}
 => 4
{{1,2,3,5},{4}}
 => {{1,3,4,5},{2}}
 => 4
{{1,2,3},{4,5}}
 => {{1,2},{3,4,5}}
 => 1
{{1,2,3},{4},{5}}
 => {{1},{2},{3,4,5}}
 => 1
{{1,2,4,5},{3}}
 => {{1,2,4,5},{3}}
 => 4
{{1,2,4},{3,5}}
 => {{1,3},{2,4,5}}
 => 1
{{1,2,4},{3},{5}}
 => {{1},{2,4,5},{3}}
 => 1
{{1,2,5},{3,4}}
 => {{1,4,5},{2,3}}
 => 1
{{1,2},{3,4,5}}
 => {{1,2,3},{4,5}}
 => 1
{{1,2},{3,4},{5}}
 => {{1},{2,3},{4,5}}
 => 0
{{1,2,5},{3},{4}}
 => {{1,4,5},{2},{3}}
 => 1
{{1,2},{3,5},{4}}
 => {{1,3},{2},{4,5}}
 => 0
{{1,2},{3},{4,5}}
 => {{1,2},{3},{4,5}}
 => 0
{{1,2},{3},{4},{5}}
 => {{1},{2},{3},{4,5}}
 => 0
{{1,3,4,5},{2}}
 => {{1,2,3,5},{4}}
 => 4
{{1,3,4},{2,5}}
 => {{1,4},{2,3,5}}
 => 1
{{1,3,4},{2},{5}}
 => {{1},{2,3,5},{4}}
 => 1
{{1,3,5},{2,4}}
 => {{1,3,5},{2,4}}
 => 1
{{1,3},{2,4,5}}
 => {{1,2,4},{3,5}}
 => 1
{{1,3},{2,4},{5}}
 => {{1},{2,4},{3,5}}
 => 0
{{1,3,5},{2},{4}}
 => {{1,3,5},{2},{4}}
 => 1
{{1,3},{2,5},{4}}
 => {{1,4},{2},{3,5}}
 => 0
{{1,3},{2},{4,5}}
 => {{1,2},{3,5},{4}}
 => 0
{{1,3},{2},{4},{5}}
 => {{1},{2},{3,5},{4}}
 => 0
{{1,4,5},{2,3}}
 => {{1,2,5},{3,4}}
 => 1
{{1,4},{2,3,5}}
 => {{1,3,4},{2,5}}
 => 1
{{1,4},{2,3},{5}}
 => {{1},{2,5},{3,4}}
 => 0
{{1,2},{3,4},{5,6},{7,8}}
 => {{1,2},{3,4},{5,6},{7,8}}
 => ? = 0
{{1,3},{2,4},{5,6},{7,8}}
 => {{1,2},{3,4},{5,7},{6,8}}
 => ? = 0
{{1,4},{2,3},{5,6},{7,8}}
 => {{1,2},{3,4},{5,8},{6,7}}
 => ? = 0
{{1,5},{2,3},{4,6},{7,8}}
 => {{1,2},{3,5},{4,8},{6,7}}
 => ? = 0
{{1,6},{2,3},{4,5},{7,8}}
 => {{1,2},{3,8},{4,5},{6,7}}
 => ? = 0
{{1,7},{2,3},{4,5},{6,8}}
 => {{1,3},{2,8},{4,5},{6,7}}
 => ? = 0
{{1,8},{2,3},{4,5},{6,7}}
 => {{1,8},{2,3},{4,5},{6,7}}
 => ? = 0
{{1,8},{2,4},{3,5},{6,7}}
 => {{1,8},{2,3},{4,6},{5,7}}
 => ? = 0
{{1,7},{2,4},{3,5},{6,8}}
 => {{1,3},{2,8},{4,6},{5,7}}
 => ? = 0
{{1,6},{2,4},{3,5},{7,8}}
 => {{1,2},{3,8},{4,6},{5,7}}
 => ? = 0
{{1,5},{2,4},{3,6},{7,8}}
 => {{1,2},{3,6},{4,8},{5,7}}
 => ? = 0
{{1,4},{2,5},{3,6},{7,8}}
 => {{1,2},{3,6},{4,7},{5,8}}
 => ? = 0
{{1,3},{2,5},{4,6},{7,8}}
 => {{1,2},{3,5},{4,7},{6,8}}
 => ? = 0
{{1,2},{3,5},{4,6},{7,8}}
 => {{1,2},{3,5},{4,6},{7,8}}
 => ? = 0
{{1,2},{3,6},{4,5},{7,8}}
 => {{1,2},{3,6},{4,5},{7,8}}
 => ? = 0
{{1,3},{2,6},{4,5},{7,8}}
 => {{1,2},{3,7},{4,5},{6,8}}
 => ? = 0
{{1,4},{2,6},{3,5},{7,8}}
 => {{1,2},{3,7},{4,6},{5,8}}
 => ? = 0
{{1,5},{2,6},{3,4},{7,8}}
 => {{1,2},{3,7},{4,8},{5,6}}
 => ? = 0
{{1,6},{2,5},{3,4},{7,8}}
 => {{1,2},{3,8},{4,7},{5,6}}
 => ? = 0
{{1,7},{2,5},{3,4},{6,8}}
 => {{1,3},{2,8},{4,7},{5,6}}
 => ? = 0
{{1,8},{2,5},{3,4},{6,7}}
 => {{1,8},{2,3},{4,7},{5,6}}
 => ? = 0
{{1,8},{2,6},{3,4},{5,7}}
 => {{1,8},{2,4},{3,7},{5,6}}
 => ? = 0
{{1,7},{2,6},{3,4},{5,8}}
 => {{1,4},{2,8},{3,7},{5,6}}
 => ? = 0
{{1,6},{2,7},{3,4},{5,8}}
 => {{1,4},{2,7},{3,8},{5,6}}
 => ? = 0
{{1,5},{2,7},{3,4},{6,8}}
 => {{1,3},{2,7},{4,8},{5,6}}
 => ? = 0
{{1,4},{2,7},{3,5},{6,8}}
 => {{1,3},{2,7},{4,6},{5,8}}
 => ? = 0
{{1,3},{2,7},{4,5},{6,8}}
 => {{1,3},{2,7},{4,5},{6,8}}
 => ? = 0
{{1,2},{3,7},{4,5},{6,8}}
 => {{1,3},{2,6},{4,5},{7,8}}
 => ? = 0
{{1,2},{3,8},{4,5},{6,7}}
 => {{1,6},{2,3},{4,5},{7,8}}
 => ? = 0
{{1,3},{2,8},{4,5},{6,7}}
 => {{1,7},{2,3},{4,5},{6,8}}
 => ? = 0
{{1,4},{2,8},{3,5},{6,7}}
 => {{1,7},{2,3},{4,6},{5,8}}
 => ? = 0
{{1,5},{2,8},{3,4},{6,7}}
 => {{1,7},{2,3},{4,8},{5,6}}
 => ? = 0
{{1,6},{2,8},{3,4},{5,7}}
 => {{1,7},{2,4},{3,8},{5,6}}
 => ? = 0
{{1,7},{2,8},{3,4},{5,6}}
 => {{1,7},{2,8},{3,4},{5,6}}
 => ? = 0
{{1,8},{2,7},{3,4},{5,6}}
 => {{1,8},{2,7},{3,4},{5,6}}
 => ? = 0
{{1,8},{2,7},{3,5},{4,6}}
 => {{1,8},{2,7},{3,5},{4,6}}
 => ? = 0
{{1,7},{2,8},{3,5},{4,6}}
 => {{1,7},{2,8},{3,5},{4,6}}
 => ? = 0
{{1,6},{2,8},{3,5},{4,7}}
 => {{1,7},{2,5},{3,8},{4,6}}
 => ? = 0
{{1,5},{2,8},{3,6},{4,7}}
 => {{1,7},{2,5},{3,6},{4,8}}
 => ? = 0
{{1,4},{2,8},{3,6},{5,7}}
 => {{1,7},{2,4},{3,6},{5,8}}
 => ? = 0
{{1,3},{2,8},{4,6},{5,7}}
 => {{1,7},{2,4},{3,5},{6,8}}
 => ? = 0
{{1,2},{3,8},{4,6},{5,7}}
 => {{1,6},{2,4},{3,5},{7,8}}
 => ? = 0
{{1,2},{3,7},{4,6},{5,8}}
 => {{1,4},{2,6},{3,5},{7,8}}
 => ? = 0
{{1,3},{2,7},{4,6},{5,8}}
 => {{1,4},{2,7},{3,5},{6,8}}
 => ? = 0
{{1,4},{2,7},{3,6},{5,8}}
 => {{1,4},{2,7},{3,6},{5,8}}
 => ? = 0
{{1,5},{2,7},{3,6},{4,8}}
 => {{1,5},{2,7},{3,6},{4,8}}
 => ? = 0
{{1,6},{2,7},{3,5},{4,8}}
 => {{1,5},{2,7},{3,8},{4,6}}
 => ? = 0
{{1,7},{2,6},{3,5},{4,8}}
 => {{1,5},{2,8},{3,7},{4,6}}
 => ? = 0
{{1,8},{2,6},{3,5},{4,7}}
 => {{1,8},{2,5},{3,7},{4,6}}
 => ? = 0
Description
The number of occurrences of the pattern {{1,2,3}} in a set partition.
Matching statistic: St001411
Mapping
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St001411: Permutations ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 46%
Values
{{1}}
 => [1] => [1,0]
 => [1] => 0
{{1,2}}
 => [2] => [1,1,0,0]
 => [2,1] => 0
{{1},{2}}
 => [1,1] => [1,0,1,0]
 => [1,2] => 0
{{1,2,3}}
 => [3] => [1,1,1,0,0,0]
 => [3,2,1] => 1
{{1,2},{3}}
 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 0
{{1,3},{2}}
 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 0
{{1},{2,3}}
 => [1,2] => [1,0,1,1,0,0]
 => [1,3,2] => 0
{{1},{2},{3}}
 => [1,1,1] => [1,0,1,0,1,0]
 => [1,2,3] => 0
{{1,2,3,4}}
 => [4] => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 4
{{1,2,3},{4}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,2,4},{3}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,2},{3,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1,2},{3},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1,3,4},{2}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,3},{2,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1,3},{2},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1,4},{2,3}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1},{2,3,4}}
 => [1,3] => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 1
{{1},{2,3},{4}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
{{1,4},{2},{3}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1},{2,4},{3}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
{{1},{2},{3,4}}
 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 0
{{1},{2},{3},{4}}
 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => 10
{{1,2,3,4},{5}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,3,5},{4}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,3},{4,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2,3},{4},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2,4,5},{3}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,4},{3,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2,4},{3},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2,5},{3,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2},{3,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,2},{3,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2,5},{3},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2},{3,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2},{3},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 0
{{1,2},{3},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 0
{{1,3,4,5},{2}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,3,4},{2,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,3,4},{2},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,3,5},{2,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,3},{2,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,3},{2,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,3,5},{2},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,3},{2,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,3},{2},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 0
{{1,3},{2},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 0
{{1,4,5},{2,3}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,4},{2,3,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,2,3,4,5,6,7}}
 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [7,6,5,4,3,2,1] => ? = 35
{{1,2,3,4,5,6},{7}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,5,7},{6}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,5},{6,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,5},{6},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4,6,7},{5}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,6},{5,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,6},{5},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4,7},{5,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,7},{5},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4},{5},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,5,6,7},{4}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,5,6},{4,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,5,6},{4},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,5,7},{4,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,5,7},{4},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,5},{4},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,6,7},{4,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,6,7},{4},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,6},{4},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,7},{4},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3},{4},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,4,5,6,7},{3}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,4,5,6},{3,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,5,6},{3},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,5,7},{3,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,5,7},{3},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,5},{3},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4,6,7},{3,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,6,7},{3},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,6},{3},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4,7},{3},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4},{3},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,5,6,7},{3,4}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2},{3,4,5,6,7}}
 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [2,1,7,6,5,4,3] => ? = 10
{{1,2,5,6,7},{3},{4}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,5,6},{3},{4},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,5,7},{3},{4},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,5},{3},{4},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,6,7},{3},{4},{5}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,6},{3},{4},{5},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,7},{3},{4},{5},{6}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2},{3},{4},{5},{6},{7}}
 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [2,1,3,4,5,6,7] => ? = 0
{{1,3,4,5,6,7},{2}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,3,4,5,6},{2,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,3,4,5,6},{2},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,3,4,5,7},{2,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,3,4,5,7},{2},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,3,4,5},{2},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,3,4,6,7},{2,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
Description
The number of patterns 321 or 3412 in a permutation. A permutation is '''boolean''' if its principal order ideal in the (strong) Bruhat order is boolean. It is shown in [1, Theorem 5.3] that a permutation is boolean if and only if it avoids the two patterns 321 and 3412.
Matching statistic: St000436
Mapping
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St000436: Permutations ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 46%
Values
{{1}}
 => [1] => [1,0]
 => [1] => ? = 0
{{1,2}}
 => [2] => [1,1,0,0]
 => [2,1] => 0
{{1},{2}}
 => [1,1] => [1,0,1,0]
 => [1,2] => 0
{{1,2,3}}
 => [3] => [1,1,1,0,0,0]
 => [3,2,1] => 1
{{1,2},{3}}
 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 0
{{1,3},{2}}
 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 0
{{1},{2,3}}
 => [1,2] => [1,0,1,1,0,0]
 => [1,3,2] => 0
{{1},{2},{3}}
 => [1,1,1] => [1,0,1,0,1,0]
 => [1,2,3] => 0
{{1,2,3,4}}
 => [4] => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 4
{{1,2,3},{4}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,2,4},{3}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,2},{3,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1,2},{3},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1,3,4},{2}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,3},{2,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1,3},{2},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1,4},{2,3}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1},{2,3,4}}
 => [1,3] => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 1
{{1},{2,3},{4}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
{{1,4},{2},{3}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1},{2,4},{3}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
{{1},{2},{3,4}}
 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 0
{{1},{2},{3},{4}}
 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => 10
{{1,2,3,4},{5}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,3,5},{4}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,3},{4,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2,3},{4},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2,4,5},{3}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,4},{3,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2,4},{3},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2,5},{3,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2},{3,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,2},{3,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2,5},{3},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2},{3,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2},{3},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 0
{{1,2},{3},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 0
{{1,3,4,5},{2}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,3,4},{2,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,3,4},{2},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,3,5},{2,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,3},{2,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,3},{2,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,3,5},{2},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,3},{2,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,3},{2},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 0
{{1,3},{2},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 0
{{1,4,5},{2,3}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,4},{2,3,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,4},{2,3},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2,3,4,5,6,7}}
 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [7,6,5,4,3,2,1] => ? = 35
{{1,2,3,4,5,6},{7}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,5,7},{6}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,5},{6,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,5},{6},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4,6,7},{5}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,6},{5,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,6},{5},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4,7},{5,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,7},{5},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4},{5},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,5,6,7},{4}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,5,6},{4,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,5,6},{4},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,5,7},{4,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,5,7},{4},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,5},{4},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,6,7},{4,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,6,7},{4},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,6},{4},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,7},{4},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3},{4},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,4,5,6,7},{3}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,4,5,6},{3,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,5,6},{3},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,5,7},{3,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,5,7},{3},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,5},{3},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4,6,7},{3,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,6,7},{3},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,6},{3},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4,7},{3},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4},{3},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,5,6,7},{3,4}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2},{3,4,5,6,7}}
 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [2,1,7,6,5,4,3] => ? = 10
{{1,2,5,6,7},{3},{4}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,5,6},{3},{4},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,5,7},{3},{4},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,5},{3},{4},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,6,7},{3},{4},{5}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,6},{3},{4},{5},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,7},{3},{4},{5},{6}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2},{3},{4},{5},{6},{7}}
 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [2,1,3,4,5,6,7] => ? = 0
{{1,3,4,5,6,7},{2}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,3,4,5,6},{2,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,3,4,5,6},{2},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,3,4,5,7},{2,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,3,4,5,7},{2},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,3,4,5},{2},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
Description
The number of occurrences of the pattern 231 or of the pattern 321 in a permutation.
Matching statistic: St000437
Mapping
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St000437: Permutations ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 46%
Values
{{1}}
 => [1] => [1,0]
 => [1] => ? = 0
{{1,2}}
 => [2] => [1,1,0,0]
 => [2,1] => 0
{{1},{2}}
 => [1,1] => [1,0,1,0]
 => [1,2] => 0
{{1,2,3}}
 => [3] => [1,1,1,0,0,0]
 => [3,2,1] => 1
{{1,2},{3}}
 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 0
{{1,3},{2}}
 => [2,1] => [1,1,0,0,1,0]
 => [2,1,3] => 0
{{1},{2,3}}
 => [1,2] => [1,0,1,1,0,0]
 => [1,3,2] => 0
{{1},{2},{3}}
 => [1,1,1] => [1,0,1,0,1,0]
 => [1,2,3] => 0
{{1,2,3,4}}
 => [4] => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 4
{{1,2,3},{4}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,2,4},{3}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,2},{3,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1,2},{3},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1,3,4},{2}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 1
{{1,3},{2,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1,3},{2},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1,4},{2,3}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 0
{{1},{2,3,4}}
 => [1,3] => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 1
{{1},{2,3},{4}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
{{1,4},{2},{3}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
{{1},{2,4},{3}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 0
{{1},{2},{3,4}}
 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 0
{{1},{2},{3},{4}}
 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => 10
{{1,2,3,4},{5}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,3,5},{4}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,3},{4,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2,3},{4},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2,4,5},{3}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,2,4},{3,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2,4},{3},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2,5},{3,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,2},{3,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,2},{3,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2,5},{3},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,2},{3,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2},{3},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 0
{{1,2},{3},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 0
{{1,3,4,5},{2}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 4
{{1,3,4},{2,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,3,4},{2},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,3,5},{2,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,3},{2,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,3},{2,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,3,5},{2},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 1
{{1,3},{2,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,3},{2},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 0
{{1,3},{2},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 0
{{1,4,5},{2,3}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 1
{{1,4},{2,3,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 1
{{1,4},{2,3},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 0
{{1,2,3,4,5,6,7}}
 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [7,6,5,4,3,2,1] => ? = 35
{{1,2,3,4,5,6},{7}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,5,7},{6}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,5},{6,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,5},{6},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4,6,7},{5}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,4,6},{5,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,6},{5},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4,7},{5,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,4,7},{5},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,4},{5},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,5,6,7},{4}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,3,5,6},{4,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,5,6},{4},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,5,7},{4,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,5,7},{4},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,5},{4},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,6,7},{4,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,3,6,7},{4},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,3,6},{4},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3,7},{4},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,3},{4},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,4,5,6,7},{3}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,2,4,5,6},{3,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,5,6},{3},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,5,7},{3,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,5,7},{3},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,5},{3},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4,6,7},{3,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2,4,6,7},{3},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,4,6},{3},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4,7},{3},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,4},{3},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,5,6,7},{3,4}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,2},{3,4,5,6,7}}
 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [2,1,7,6,5,4,3] => ? = 10
{{1,2,5,6,7},{3},{4}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,2,5,6},{3},{4},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,5,7},{3},{4},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,5},{3},{4},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,6,7},{3},{4},{5}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
{{1,2,6},{3},{4},{5},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2,7},{3},{4},{5},{6}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6,7] => ? = 1
{{1,2},{3},{4},{5},{6},{7}}
 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [2,1,3,4,5,6,7] => ? = 0
{{1,3,4,5,6,7},{2}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => ? = 20
{{1,3,4,5,6},{2,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,3,4,5,6},{2},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,3,4,5,7},{2,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,4,3,2,1,7,6] => ? = 10
{{1,3,4,5,7},{2},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [5,4,3,2,1,6,7] => ? = 10
{{1,3,4,5},{2},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [4,3,2,1,5,6,7] => ? = 4
Description
The number of occurrences of the pattern 312 or of the pattern 321 in a permutation.
Matching statistic: St000423
(load all 2 compositions to match this statistic)
Mapping
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000423: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 54%
Values
{{1}}
 => [1] => [1,0]
 => [1] => 0
{{1,2}}
 => [2] => [1,1,0,0]
 => [1,2] => 0
{{1},{2}}
 => [1,1] => [1,0,1,0]
 => [2,1] => 0
{{1,2,3}}
 => [3] => [1,1,1,0,0,0]
 => [1,2,3] => 1
{{1,2},{3}}
 => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 0
{{1,3},{2}}
 => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 0
{{1},{2,3}}
 => [1,2] => [1,0,1,1,0,0]
 => [2,3,1] => 0
{{1},{2},{3}}
 => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 0
{{1,2,3,4}}
 => [4] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 4
{{1,2,3},{4}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,2,4},{3}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,2},{3,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1,2},{3},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1,3,4},{2}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,3},{2,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1,3},{2},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1,4},{2,3}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1},{2,3,4}}
 => [1,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 1
{{1},{2,3},{4}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 0
{{1,4},{2},{3}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1},{2,4},{3}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 0
{{1},{2},{3,4}}
 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 0
{{1},{2},{3},{4}}
 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 0
{{1,2,3,4,5}}
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => 10
{{1,2,3,4},{5}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,3,5},{4}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,3},{4,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2,3},{4},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2,4,5},{3}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,4},{3,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2,4},{3},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2,5},{3,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2},{3,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1,2},{3,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,2,5},{3},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2},{3,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,2},{3},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 0
{{1,2},{3},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 0
{{1,3,4,5},{2}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,3,4},{2,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,3,4},{2},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,3,5},{2,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,3},{2,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1,3},{2,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,3,5},{2},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,3},{2,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,3},{2},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 0
{{1,3},{2},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 0
{{1,4,5},{2,3}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,4},{2,3,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1,2,3,4,5,6},{7}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,3,4,5,7},{6}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,3,4,5},{6,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,4,5},{6},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,4,6,7},{5}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,3,4,6},{5,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,4,6},{5},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,4,7},{5,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,4,7},{5},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,4},{5},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,3,5,6,7},{4}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,3,5,6},{4,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,5,6},{4},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,5,7},{4,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,5,7},{4},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,5},{4},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,3,6,7},{4,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,6,7},{4},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,6},{4},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,3,7},{4},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,3},{4},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2,4,5,6,7},{3}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,4,5,6},{3,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,4,5,6},{3},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,4,5,7},{3,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,4,5,7},{3},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,4,5},{3},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,4,6,7},{3,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,4,6,7},{3},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,4,6},{3},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,4,7},{3},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,4},{3},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2,5,6,7},{3,4}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2},{3,4,5,6,7}}
 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [3,4,5,6,7,1,2] => ? = 10
{{1,2,5,6,7},{3},{4}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,5,6},{3},{4},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,5,7},{3},{4},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,5},{3},{4},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2,6,7},{3},{4},{5}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,6},{3},{4},{5},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2,7},{3},{4},{5},{6}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2},{3},{4},{5},{6},{7}}
 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,3,1,2] => ? = 0
{{1,3,4,5,6,7},{2}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,3,4,5,6},{2,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,3,4,5,6},{2},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,3,4,5,7},{2,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,3,4,5,7},{2},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,3,4,5},{2},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,3,4,6,7},{2,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,3,4,6,7},{2},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
Description
The number of occurrences of the pattern 123 or of the pattern 132 in a permutation.
Matching statistic: St000428
(load all 2 compositions to match this statistic)
Mapping
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000428: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 54%
Values
{{1}}
 => [1] => [1,0]
 => [1] => 0
{{1,2}}
 => [2] => [1,1,0,0]
 => [1,2] => 0
{{1},{2}}
 => [1,1] => [1,0,1,0]
 => [2,1] => 0
{{1,2,3}}
 => [3] => [1,1,1,0,0,0]
 => [1,2,3] => 1
{{1,2},{3}}
 => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 0
{{1,3},{2}}
 => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 0
{{1},{2,3}}
 => [1,2] => [1,0,1,1,0,0]
 => [2,3,1] => 0
{{1},{2},{3}}
 => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 0
{{1,2,3,4}}
 => [4] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 4
{{1,2,3},{4}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,2,4},{3}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,2},{3,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1,2},{3},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1,3,4},{2}}
 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
{{1,3},{2,4}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1,3},{2},{4}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1,4},{2,3}}
 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
{{1},{2,3,4}}
 => [1,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 1
{{1},{2,3},{4}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 0
{{1,4},{2},{3}}
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 0
{{1},{2,4},{3}}
 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 0
{{1},{2},{3,4}}
 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 0
{{1},{2},{3},{4}}
 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 0
{{1,2,3,4,5}}
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => 10
{{1,2,3,4},{5}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,3,5},{4}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,3},{4,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2,3},{4},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2,4,5},{3}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,2,4},{3,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2,4},{3},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2,5},{3,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,2},{3,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1,2},{3,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,2,5},{3},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,2},{3,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,2},{3},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 0
{{1,2},{3},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 0
{{1,3,4,5},{2}}
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 4
{{1,3,4},{2,5}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,3,4},{2},{5}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,3,5},{2,4}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,3},{2,4,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1,3},{2,4},{5}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,3,5},{2},{4}}
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
{{1,3},{2,5},{4}}
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 0
{{1,3},{2},{4,5}}
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 0
{{1,3},{2},{4},{5}}
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 0
{{1,4,5},{2,3}}
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 1
{{1,4},{2,3,5}}
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 1
{{1,2,3,4,5,6},{7}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,3,4,5,7},{6}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,3,4,5},{6,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,4,5},{6},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,4,6,7},{5}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,3,4,6},{5,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,4,6},{5},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,4,7},{5,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,4,7},{5},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,4},{5},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,3,5,6,7},{4}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,3,5,6},{4,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,5,6},{4},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,5,7},{4,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,5,7},{4},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,5},{4},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,3,6,7},{4,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,3,6,7},{4},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,3,6},{4},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,3,7},{4},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,3},{4},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2,4,5,6,7},{3}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,2,4,5,6},{3,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,4,5,6},{3},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,4,5,7},{3,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,4,5,7},{3},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,4,5},{3},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,4,6,7},{3,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2,4,6,7},{3},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,4,6},{3},{5},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,4,7},{3},{5},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,4},{3},{5},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2,5,6,7},{3,4}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,2},{3,4,5,6,7}}
 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [3,4,5,6,7,1,2] => ? = 10
{{1,2,5,6,7},{3},{4}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,2,5,6},{3},{4},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,5,7},{3},{4},{6}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,5},{3},{4},{6},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2,6,7},{3},{4},{5}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,2,6},{3},{4},{5},{7}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2,7},{3},{4},{5},{6}}
 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,1,2,3] => ? = 1
{{1,2},{3},{4},{5},{6},{7}}
 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [7,6,5,4,3,1,2] => ? = 0
{{1,3,4,5,6,7},{2}}
 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => ? = 20
{{1,3,4,5,6},{2,7}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,3,4,5,6},{2},{7}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,3,4,5,7},{2,6}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,3,4,5,7},{2},{6}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
{{1,3,4,5},{2},{6},{7}}
 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [7,6,5,1,2,3,4] => ? = 4
{{1,3,4,6,7},{2,5}}
 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => ? = 10
{{1,3,4,6,7},{2},{5}}
 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [7,6,1,2,3,4,5] => ? = 10
Description
The number of occurrences of the pattern 123 or of the pattern 213 in a permutation.