Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001587
(load all 3 compositions to match this statistic)
Mapping
St001587: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 0
[2]
 => 1
[1,1]
 => 0
[3]
 => 0
[2,1]
 => 1
[1,1,1]
 => 0
[4]
 => 2
[3,1]
 => 0
[2,2]
 => 1
[2,1,1]
 => 1
[1,1,1,1]
 => 0
[5]
 => 0
[4,1]
 => 2
[3,2]
 => 1
[3,1,1]
 => 0
[2,2,1]
 => 1
[2,1,1,1]
 => 1
[1,1,1,1,1]
 => 0
[6]
 => 3
[5,1]
 => 0
[4,2]
 => 2
[4,1,1]
 => 2
[3,2,1]
 => 1
[3,1,1,1]
 => 0
[2,2,1,1]
 => 1
[2,1,1,1,1]
 => 1
[1,1,1,1,1,1]
 => 0
[6,1]
 => 3
[5,2]
 => 1
[5,1,1]
 => 0
[4,3]
 => 2
[4,2,1]
 => 2
[4,1,1,1]
 => 2
[3,2,2]
 => 1
[3,2,1,1]
 => 1
[3,1,1,1,1]
 => 0
[2,1,1,1,1,1]
 => 1
[1,1,1,1,1,1,1]
 => 0
[8]
 => 4
[6,2]
 => 3
[6,1,1]
 => 3
[5,3]
 => 0
[5,2,1]
 => 1
[5,1,1,1]
 => 0
[4,4]
 => 2
[4,3,1]
 => 2
[4,2,1,1]
 => 2
[4,1,1,1,1]
 => 2
[3,2,1,1,1]
 => 1
[3,1,1,1,1,1]
 => 0
Description
Half of the largest even part of an integer partition. The largest even part is recorded by [[St000995]].
Matching statistic: St001685
(load all 2 compositions to match this statistic)
Mapping
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
St001685: 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] => 0
[2]
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1
[1,1]
 => [2]
 => [1,1,0,0,1,0]
 => [2,1,3] => 0
[3]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 0
[2,1]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 1
[1,1,1]
 => [2,1]
 => [1,0,1,0,1,0]
 => [1,2,3] => 0
[4]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 2
[3,1]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [2,3,1,4] => 0
[2,2]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => 1
[2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,3,4,2] => 1
[1,1,1,1]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => 0
[5]
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,4,3,2,1,6] => 0
[4,1]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 2
[3,2]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 1
[3,1,1]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 0
[2,2,1]
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,6,5,4,3,2] => 1
[2,1,1,1]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,3,2] => 1
[1,1,1,1,1]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [3,4,2,1,5] => 0
[6]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => 3
[5,1]
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [4,5,3,2,1,6] => 0
[4,2]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => 2
[4,1,1]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 2
[3,2,1]
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => 1
[3,1,1,1]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
[2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,5,6,4,3,2] => 1
[2,1,1,1,1]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => 1
[1,1,1,1,1,1]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => 0
[6,1]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => 3
[5,2]
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [3,5,4,2,1,6] => 1
[5,1,1]
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [4,3,5,2,1,6] => 0
[4,3]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => 2
[4,2,1]
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,4,6,5,3,2] => 2
[4,1,1,1]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => 2
[3,2,2]
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,5,4,6,3,2] => 1
[3,2,1,1]
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => 1
[3,1,1,1,1]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => 0
[2,1,1,1,1,1]
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => 1
[1,1,1,1,1,1,1]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => 0
[8]
 => [4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,3,2,1,6,5] => 4
[6,2]
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => 3
[6,1,1]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 3
[5,3]
 => [5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [4,3,2,5,1,6] => 0
[5,2,1]
 => [5,1,1,1]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [2,5,4,3,1,6] => 1
[5,1,1,1]
 => [5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [3,4,5,2,1,6] => 0
[4,4]
 => [2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,6,5,4,3] => 2
[4,3,1]
 => [3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => 2
[4,2,1,1]
 => [2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,3,6,5,4,2] => 2
[4,1,1,1,1]
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 2
[3,2,1,1,1]
 => [3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,4,5,6,3,2] => 1
[3,1,1,1,1,1]
 => [4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => 0
Description
The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation.
Matching statistic: St000143
Mapping
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
St000143: Integer partitions ⟶ ℤResult quality: 64% ●values known / values provided: 64%●distinct values known / distinct values provided: 83%
Values
[1]
 => [1]
 => 0
[2]
 => [1,1]
 => 1
[1,1]
 => [2]
 => 0
[3]
 => [3]
 => 0
[2,1]
 => [1,1,1]
 => 1
[1,1,1]
 => [2,1]
 => 0
[4]
 => [2,2]
 => 2
[3,1]
 => [3,1]
 => 0
[2,2]
 => [1,1,1,1]
 => 1
[2,1,1]
 => [2,1,1]
 => 1
[1,1,1,1]
 => [4]
 => 0
[5]
 => [5]
 => 0
[4,1]
 => [2,2,1]
 => 2
[3,2]
 => [3,1,1]
 => 1
[3,1,1]
 => [3,2]
 => 0
[2,2,1]
 => [1,1,1,1,1]
 => 1
[2,1,1,1]
 => [2,1,1,1]
 => 1
[1,1,1,1,1]
 => [4,1]
 => 0
[6]
 => [3,3]
 => 3
[5,1]
 => [5,1]
 => 0
[4,2]
 => [2,2,1,1]
 => 2
[4,1,1]
 => [2,2,2]
 => 2
[3,2,1]
 => [3,1,1,1]
 => 1
[3,1,1,1]
 => [3,2,1]
 => 0
[2,2,1,1]
 => [2,1,1,1,1]
 => 1
[2,1,1,1,1]
 => [4,1,1]
 => 1
[1,1,1,1,1,1]
 => [4,2]
 => 0
[6,1]
 => [3,3,1]
 => 3
[5,2]
 => [5,1,1]
 => 1
[5,1,1]
 => [5,2]
 => 0
[4,3]
 => [3,2,2]
 => 2
[4,2,1]
 => [2,2,1,1,1]
 => 2
[4,1,1,1]
 => [2,2,2,1]
 => 2
[3,2,2]
 => [3,1,1,1,1]
 => 1
[3,2,1,1]
 => [3,2,1,1]
 => 1
[3,1,1,1,1]
 => [4,3]
 => 0
[2,1,1,1,1,1]
 => [4,1,1,1]
 => 1
[1,1,1,1,1,1,1]
 => [4,2,1]
 => 0
[8]
 => [4,4]
 => 4
[6,2]
 => [3,3,1,1]
 => 3
[6,1,1]
 => [3,3,2]
 => 3
[5,3]
 => [5,3]
 => 0
[5,2,1]
 => [5,1,1,1]
 => 1
[5,1,1,1]
 => [5,2,1]
 => 0
[4,4]
 => [2,2,2,2]
 => 2
[4,3,1]
 => [3,2,2,1]
 => 2
[4,2,1,1]
 => [2,2,2,1,1]
 => 2
[4,1,1,1,1]
 => [4,2,2]
 => 2
[3,2,1,1,1]
 => [3,2,1,1,1]
 => 1
[3,1,1,1,1,1]
 => [4,3,1]
 => 0
[6,2,1,1,1]
 => [3,3,2,1,1,1]
 => ? = 3
[4,4,1,1,1]
 => [2,2,2,2,2,1]
 => ? = 2
[4,3,2,1,1]
 => [3,2,2,2,1,1]
 => ? = 2
[6,3,2,1]
 => [3,3,3,1,1,1]
 => ? = 3
[4,4,3,1]
 => [3,2,2,2,2,1]
 => ? = 2
[4,2,1,1,1,1,1,1]
 => [4,2,2,2,1,1]
 => ? = 2
[3,2,1,1,1,1,1,1,1]
 => [4,3,2,1,1,1]
 => ? = 1
[8,2,1,1,1]
 => [4,4,2,1,1,1]
 => ? = 4
[6,4,1,1,1]
 => [3,3,2,2,2,1]
 => ? = 3
[6,3,2,1,1]
 => [3,3,3,2,1,1]
 => ? = 3
[6,2,1,1,1,1,1]
 => [4,3,3,1,1,1]
 => ? = 3
[5,4,2,1,1]
 => [5,2,2,2,1,1]
 => ? = 2
[5,3,2,1,1,1]
 => [5,3,2,1,1,1]
 => ? = 1
[4,4,1,1,1,1,1]
 => [4,2,2,2,2,1]
 => ? = 2
[4,3,3,2,1]
 => [6,2,2,1,1,1]
 => ? = 2
[4,3,2,1,1,1,1]
 => [4,3,2,2,1,1]
 => ? = 2
[8,4,2]
 => [4,4,2,2,1,1]
 => ? = 4
[8,3,2,1]
 => [4,4,3,1,1,1]
 => ? = 4
[6,6,2]
 => [3,3,3,3,1,1]
 => ? = 3
[6,5,2,1]
 => [5,3,3,1,1,1]
 => ? = 3
[6,4,3,1]
 => [3,3,3,2,2,1]
 => ? = 3
[6,2,1,1,1,1,1,1]
 => [4,3,3,2,1,1]
 => ? = 3
[5,4,4,1]
 => [5,2,2,2,2,1]
 => ? = 2
[5,4,3,2]
 => [5,3,2,2,1,1]
 => ? = 2
[5,2,1,1,1,1,1,1,1]
 => [5,4,2,1,1,1]
 => ? = 1
[4,3,3,2,1,1]
 => [6,2,2,2,1,1]
 => ? = 2
[4,3,1,1,1,1,1,1,1]
 => [4,3,2,2,2,1]
 => ? = 2
[3,3,3,2,1,1,1]
 => [6,3,2,1,1,1]
 => ? = 1
[10,2,1,1,1]
 => [5,5,2,1,1,1]
 => ? = 5
[8,4,1,1,1]
 => [4,4,2,2,2,1]
 => ? = 4
[8,3,2,1,1]
 => [4,4,3,2,1,1]
 => ? = 4
[8,2,1,1,1,1,1]
 => [4,4,4,1,1,1]
 => ? = 4
[6,6,1,1,1]
 => [3,3,3,3,2,1]
 => ? = 3
[6,5,2,1,1]
 => [5,3,3,2,1,1]
 => ? = 3
[6,4,1,1,1,1,1]
 => [4,3,3,2,2,1]
 => ? = 3
[6,3,3,2,1]
 => [6,3,3,1,1,1]
 => ? = 3
[6,3,2,1,1,1,1]
 => [4,3,3,3,1,1]
 => ? = 3
[5,4,3,1,1,1]
 => [5,3,2,2,2,1]
 => ? = 2
[5,4,2,1,1,1,1]
 => [5,4,2,2,1,1]
 => ? = 2
[5,3,2,1,1,1,1,1]
 => [5,4,3,1,1,1]
 => ? = 1
[4,4,3,3,1]
 => [6,2,2,2,2,1]
 => ? = 2
[4,3,3,3,2]
 => [6,3,2,2,1,1]
 => ? = 2
[3,3,2,1,1,1,1,1,1,1]
 => [6,4,2,1,1,1]
 => ? = 1
[10,4,2]
 => [5,5,2,2,1,1]
 => ? = 5
[10,3,2,1]
 => [5,5,3,1,1,1]
 => ? = 5
[8,6,2]
 => [4,4,3,3,1,1]
 => ? = 4
[8,5,2,1]
 => [5,4,4,1,1,1]
 => ? = 4
[8,4,3,1]
 => [4,4,3,2,2,1]
 => ? = 4
[8,2,1,1,1,1,1,1]
 => [4,4,4,2,1,1]
 => ? = 4
[6,5,4,1]
 => [5,3,3,2,2,1]
 => ? = 3
Description
The largest repeated part of a partition. If the parts of the partition are all distinct, the value of the statistic is defined to be zero.
Matching statistic: St001801
Mapping
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St001801: Permutations ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 67%
Values
[1]
 => [[1]]
 => [[1]]
 => [1] => 0
[2]
 => [[1,2]]
 => [[1],[2]]
 => [2,1] => 1
[1,1]
 => [[1],[2]]
 => [[1,2]]
 => [1,2] => 0
[3]
 => [[1,2,3]]
 => [[1],[2],[3]]
 => [3,2,1] => 0
[2,1]
 => [[1,2],[3]]
 => [[1,3],[2]]
 => [2,1,3] => 1
[1,1,1]
 => [[1],[2],[3]]
 => [[1,2,3]]
 => [1,2,3] => 0
[4]
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => [4,3,2,1] => 2
[3,1]
 => [[1,2,3],[4]]
 => [[1,4],[2],[3]]
 => [3,2,1,4] => 0
[2,2]
 => [[1,2],[3,4]]
 => [[1,3],[2,4]]
 => [2,4,1,3] => 1
[2,1,1]
 => [[1,2],[3],[4]]
 => [[1,3,4],[2]]
 => [2,1,3,4] => 1
[1,1,1,1]
 => [[1],[2],[3],[4]]
 => [[1,2,3,4]]
 => [1,2,3,4] => 0
[5]
 => [[1,2,3,4,5]]
 => [[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => 0
[4,1]
 => [[1,2,3,4],[5]]
 => [[1,5],[2],[3],[4]]
 => [4,3,2,1,5] => 2
[3,2]
 => [[1,2,3],[4,5]]
 => [[1,4],[2,5],[3]]
 => [3,2,5,1,4] => 1
[3,1,1]
 => [[1,2,3],[4],[5]]
 => [[1,4,5],[2],[3]]
 => [3,2,1,4,5] => 0
[2,2,1]
 => [[1,2],[3,4],[5]]
 => [[1,3,5],[2,4]]
 => [2,4,1,3,5] => 1
[2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [[1,3,4,5],[2]]
 => [2,1,3,4,5] => 1
[1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => [[1,2,3,4,5]]
 => [1,2,3,4,5] => 0
[6]
 => [[1,2,3,4,5,6]]
 => [[1],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1] => 3
[5,1]
 => [[1,2,3,4,5],[6]]
 => [[1,6],[2],[3],[4],[5]]
 => [5,4,3,2,1,6] => 0
[4,2]
 => [[1,2,3,4],[5,6]]
 => [[1,5],[2,6],[3],[4]]
 => [4,3,2,6,1,5] => 2
[4,1,1]
 => [[1,2,3,4],[5],[6]]
 => [[1,5,6],[2],[3],[4]]
 => [4,3,2,1,5,6] => 2
[3,2,1]
 => [[1,2,3],[4,5],[6]]
 => [[1,4,6],[2,5],[3]]
 => [3,2,5,1,4,6] => 1
[3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,4,5,6],[2],[3]]
 => [3,2,1,4,5,6] => 0
[2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3,5,6],[2,4]]
 => [2,4,1,3,5,6] => 1
[2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3,4,5,6],[2]]
 => [2,1,3,4,5,6] => 1
[1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => [[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => 0
[6,1]
 => [[1,2,3,4,5,6],[7]]
 => [[1,7],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1,7] => ? = 3
[5,2]
 => [[1,2,3,4,5],[6,7]]
 => [[1,6],[2,7],[3],[4],[5]]
 => [5,4,3,2,7,1,6] => ? = 1
[5,1,1]
 => [[1,2,3,4,5],[6],[7]]
 => [[1,6,7],[2],[3],[4],[5]]
 => [5,4,3,2,1,6,7] => ? = 0
[4,3]
 => [[1,2,3,4],[5,6,7]]
 => [[1,5],[2,6],[3,7],[4]]
 => [4,3,7,2,6,1,5] => ? = 2
[4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [[1,5,7],[2,6],[3],[4]]
 => [4,3,2,6,1,5,7] => ? = 2
[4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [[1,5,6,7],[2],[3],[4]]
 => [4,3,2,1,5,6,7] => ? = 2
[3,2,2]
 => [[1,2,3],[4,5],[6,7]]
 => [[1,4,6],[2,5,7],[3]]
 => [3,2,5,7,1,4,6] => ? = 1
[3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [[1,4,6,7],[2,5],[3]]
 => [3,2,5,1,4,6,7] => ? = 1
[3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [[1,4,5,6,7],[2],[3]]
 => [3,2,1,4,5,6,7] => ? = 0
[2,1,1,1,1,1]
 => [[1,2],[3],[4],[5],[6],[7]]
 => [[1,3,4,5,6,7],[2]]
 => [2,1,3,4,5,6,7] => ? = 1
[1,1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => [[1,2,3,4,5,6,7]]
 => [1,2,3,4,5,6,7] => 0
[8]
 => [[1,2,3,4,5,6,7,8]]
 => [[1],[2],[3],[4],[5],[6],[7],[8]]
 => [8,7,6,5,4,3,2,1] => ? = 4
[6,2]
 => [[1,2,3,4,5,6],[7,8]]
 => [[1,7],[2,8],[3],[4],[5],[6]]
 => [6,5,4,3,2,8,1,7] => ? = 3
[6,1,1]
 => [[1,2,3,4,5,6],[7],[8]]
 => [[1,7,8],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1,7,8] => ? = 3
[5,3]
 => [[1,2,3,4,5],[6,7,8]]
 => [[1,6],[2,7],[3,8],[4],[5]]
 => [5,4,3,8,2,7,1,6] => ? = 0
[5,2,1]
 => [[1,2,3,4,5],[6,7],[8]]
 => [[1,6,8],[2,7],[3],[4],[5]]
 => [5,4,3,2,7,1,6,8] => ? = 1
[5,1,1,1]
 => [[1,2,3,4,5],[6],[7],[8]]
 => [[1,6,7,8],[2],[3],[4],[5]]
 => [5,4,3,2,1,6,7,8] => ? = 0
[4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => [[1,5],[2,6],[3,7],[4,8]]
 => [4,8,3,7,2,6,1,5] => ? = 2
[4,3,1]
 => [[1,2,3,4],[5,6,7],[8]]
 => [[1,5,8],[2,6],[3,7],[4]]
 => [4,3,7,2,6,1,5,8] => ? = 2
[4,2,1,1]
 => [[1,2,3,4],[5,6],[7],[8]]
 => [[1,5,7,8],[2,6],[3],[4]]
 => [4,3,2,6,1,5,7,8] => ? = 2
[4,1,1,1,1]
 => [[1,2,3,4],[5],[6],[7],[8]]
 => [[1,5,6,7,8],[2],[3],[4]]
 => [4,3,2,1,5,6,7,8] => ? = 2
[3,2,1,1,1]
 => [[1,2,3],[4,5],[6],[7],[8]]
 => [[1,4,6,7,8],[2,5],[3]]
 => [3,2,5,1,4,6,7,8] => ? = 1
[3,1,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7],[8]]
 => [[1,4,5,6,7,8],[2],[3]]
 => [3,2,1,4,5,6,7,8] => ? = 0
[2,2,1,1,1,1]
 => [[1,2],[3,4],[5],[6],[7],[8]]
 => [[1,3,5,6,7,8],[2,4]]
 => [2,4,1,3,5,6,7,8] => ? = 1
[2,1,1,1,1,1,1]
 => [[1,2],[3],[4],[5],[6],[7],[8]]
 => [[1,3,4,5,6,7,8],[2]]
 => [2,1,3,4,5,6,7,8] => ? = 1
[8,1]
 => [[1,2,3,4,5,6,7,8],[9]]
 => [[1,9],[2],[3],[4],[5],[6],[7],[8]]
 => [8,7,6,5,4,3,2,1,9] => ? = 4
[6,3]
 => [[1,2,3,4,5,6],[7,8,9]]
 => [[1,7],[2,8],[3,9],[4],[5],[6]]
 => [6,5,4,3,9,2,8,1,7] => ? = 3
[6,2,1]
 => [[1,2,3,4,5,6],[7,8],[9]]
 => [[1,7,9],[2,8],[3],[4],[5],[6]]
 => [6,5,4,3,2,8,1,7,9] => ? = 3
[6,1,1,1]
 => [[1,2,3,4,5,6],[7],[8],[9]]
 => [[1,7,8,9],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1,7,8,9] => ? = 3
[5,4]
 => [[1,2,3,4,5],[6,7,8,9]]
 => [[1,6],[2,7],[3,8],[4,9],[5]]
 => [5,4,9,3,8,2,7,1,6] => ? = 2
[5,3,1]
 => [[1,2,3,4,5],[6,7,8],[9]]
 => [[1,6,9],[2,7],[3,8],[4],[5]]
 => [5,4,3,8,2,7,1,6,9] => ? = 0
[5,2,2]
 => [[1,2,3,4,5],[6,7],[8,9]]
 => [[1,6,8],[2,7,9],[3],[4],[5]]
 => [5,4,3,2,7,9,1,6,8] => ? = 1
[5,2,1,1]
 => [[1,2,3,4,5],[6,7],[8],[9]]
 => [[1,6,8,9],[2,7],[3],[4],[5]]
 => [5,4,3,2,7,1,6,8,9] => ? = 1
[5,1,1,1,1]
 => [[1,2,3,4,5],[6],[7],[8],[9]]
 => [[1,6,7,8,9],[2],[3],[4],[5]]
 => [5,4,3,2,1,6,7,8,9] => ? = 0
[4,4,1]
 => [[1,2,3,4],[5,6,7,8],[9]]
 => [[1,5,9],[2,6],[3,7],[4,8]]
 => [4,8,3,7,2,6,1,5,9] => ? = 2
[4,3,2]
 => [[1,2,3,4],[5,6,7],[8,9]]
 => [[1,5,8],[2,6,9],[3,7],[4]]
 => [4,3,7,2,6,9,1,5,8] => ? = 2
[4,3,1,1]
 => [[1,2,3,4],[5,6,7],[8],[9]]
 => [[1,5,8,9],[2,6],[3,7],[4]]
 => [4,3,7,2,6,1,5,8,9] => ? = 2
[4,1,1,1,1,1]
 => [[1,2,3,4],[5],[6],[7],[8],[9]]
 => [[1,5,6,7,8,9],[2],[3],[4]]
 => [4,3,2,1,5,6,7,8,9] => ? = 2
[3,2,1,1,1,1]
 => [[1,2,3],[4,5],[6],[7],[8],[9]]
 => [[1,4,6,7,8,9],[2,5],[3]]
 => [3,2,5,1,4,6,7,8,9] => ? = 1
[3,1,1,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7],[8],[9]]
 => [[1,4,5,6,7,8,9],[2],[3]]
 => [3,2,1,4,5,6,7,8,9] => ? = 0
[2,1,1,1,1,1,1,1]
 => [[1,2],[3],[4],[5],[6],[7],[8],[9]]
 => [[1,3,4,5,6,7,8,9],[2]]
 => [2,1,3,4,5,6,7,8,9] => ? = 1
[8,2]
 => [[1,2,3,4,5,6,7,8],[9,10]]
 => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]]
 => [8,7,6,5,4,3,2,10,1,9] => ? = 4
[8,1,1]
 => [[1,2,3,4,5,6,7,8],[9],[10]]
 => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]]
 => [8,7,6,5,4,3,2,1,9,10] => ? = 4
[6,4]
 => [[1,2,3,4,5,6],[7,8,9,10]]
 => [[1,7],[2,8],[3,9],[4,10],[5],[6]]
 => [6,5,4,10,3,9,2,8,1,7] => ? = 3
[6,3,1]
 => [[1,2,3,4,5,6],[7,8,9],[10]]
 => [[1,7,10],[2,8],[3,9],[4],[5],[6]]
 => [6,5,4,3,9,2,8,1,7,10] => ? = 3
[6,2,1,1]
 => [[1,2,3,4,5,6],[7,8],[9],[10]]
 => [[1,7,9,10],[2,8],[3],[4],[5],[6]]
 => [6,5,4,3,2,8,1,7,9,10] => ? = 3
[6,1,1,1,1]
 => [[1,2,3,4,5,6],[7],[8],[9],[10]]
 => [[1,7,8,9,10],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1,7,8,9,10] => ? = 3
[5,4,1]
 => [[1,2,3,4,5],[6,7,8,9],[10]]
 => [[1,6,10],[2,7],[3,8],[4,9],[5]]
 => [5,4,9,3,8,2,7,1,6,10] => ? = 2
[5,3,2]
 => [[1,2,3,4,5],[6,7,8],[9,10]]
 => [[1,6,9],[2,7,10],[3,8],[4],[5]]
 => [5,4,3,8,2,7,10,1,6,9] => ? = 1
[5,3,1,1]
 => [[1,2,3,4,5],[6,7,8],[9],[10]]
 => [[1,6,9,10],[2,7],[3,8],[4],[5]]
 => [5,4,3,8,2,7,1,6,9,10] => ? = 0
[5,2,1,1,1]
 => [[1,2,3,4,5],[6,7],[8],[9],[10]]
 => [[1,6,8,9,10],[2,7],[3],[4],[5]]
 => [5,4,3,2,7,1,6,8,9,10] => ? = 1
Description
Half the number of preimage-image pairs of different parity in a permutation.