Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000532
(load all 3 compositions to match this statistic)
Mapping
St000532: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 2
[2]
 => 3
[1,1]
 => 3
[3]
 => 4
[2,1]
 => 5
[1,1,1]
 => 4
[4]
 => 5
[3,1]
 => 7
[2,2]
 => 7
[2,1,1]
 => 7
[1,1,1,1]
 => 5
[5]
 => 6
[4,1]
 => 9
[3,2]
 => 10
[3,1,1]
 => 10
[2,2,1]
 => 10
[2,1,1,1]
 => 9
[1,1,1,1,1]
 => 6
[6]
 => 7
[5,1]
 => 11
[4,2]
 => 13
[4,1,1]
 => 13
[3,3]
 => 13
[3,2,1]
 => 15
[3,1,1,1]
 => 13
[2,2,2]
 => 13
[2,2,1,1]
 => 13
[2,1,1,1,1]
 => 11
[1,1,1,1,1,1]
 => 7
[7]
 => 8
[6,1]
 => 13
[5,2]
 => 16
[5,1,1]
 => 16
[4,3]
 => 17
[4,2,1]
 => 20
[4,1,1,1]
 => 17
[3,3,1]
 => 20
[3,2,2]
 => 20
[3,2,1,1]
 => 20
[3,1,1,1,1]
 => 16
[2,2,2,1]
 => 17
[2,2,1,1,1]
 => 16
[2,1,1,1,1,1]
 => 13
[1,1,1,1,1,1,1]
 => 8
[8]
 => 9
[7,1]
 => 15
[6,2]
 => 19
[6,1,1]
 => 19
[5,3]
 => 21
[5,2,1]
 => 25
Description
The total number of rook placements on a Ferrers board.
Matching statistic: St001658
(load all 4 compositions to match this statistic)
Mapping
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001658: Skew partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 28%
Values
[1]
 => [[1],[]]
 => 2
[2]
 => [[2],[]]
 => 3
[1,1]
 => [[1,1],[]]
 => 3
[3]
 => [[3],[]]
 => 4
[2,1]
 => [[2,1],[]]
 => 5
[1,1,1]
 => [[1,1,1],[]]
 => 4
[4]
 => [[4],[]]
 => 5
[3,1]
 => [[3,1],[]]
 => 7
[2,2]
 => [[2,2],[]]
 => 7
[2,1,1]
 => [[2,1,1],[]]
 => 7
[1,1,1,1]
 => [[1,1,1,1],[]]
 => 5
[5]
 => [[5],[]]
 => 6
[4,1]
 => [[4,1],[]]
 => 9
[3,2]
 => [[3,2],[]]
 => 10
[3,1,1]
 => [[3,1,1],[]]
 => 10
[2,2,1]
 => [[2,2,1],[]]
 => 10
[2,1,1,1]
 => [[2,1,1,1],[]]
 => 9
[1,1,1,1,1]
 => [[1,1,1,1,1],[]]
 => 6
[6]
 => [[6],[]]
 => 7
[5,1]
 => [[5,1],[]]
 => 11
[4,2]
 => [[4,2],[]]
 => 13
[4,1,1]
 => [[4,1,1],[]]
 => 13
[3,3]
 => [[3,3],[]]
 => 13
[3,2,1]
 => [[3,2,1],[]]
 => 15
[3,1,1,1]
 => [[3,1,1,1],[]]
 => 13
[2,2,2]
 => [[2,2,2],[]]
 => 13
[2,2,1,1]
 => [[2,2,1,1],[]]
 => 13
[2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => 11
[1,1,1,1,1,1]
 => [[1,1,1,1,1,1],[]]
 => 7
[7]
 => [[7],[]]
 => 8
[6,1]
 => [[6,1],[]]
 => 13
[5,2]
 => [[5,2],[]]
 => 16
[5,1,1]
 => [[5,1,1],[]]
 => 16
[4,3]
 => [[4,3],[]]
 => 17
[4,2,1]
 => [[4,2,1],[]]
 => 20
[4,1,1,1]
 => [[4,1,1,1],[]]
 => 17
[3,3,1]
 => [[3,3,1],[]]
 => 20
[3,2,2]
 => [[3,2,2],[]]
 => 20
[3,2,1,1]
 => [[3,2,1,1],[]]
 => 20
[3,1,1,1,1]
 => [[3,1,1,1,1],[]]
 => 16
[2,2,2,1]
 => [[2,2,2,1],[]]
 => 17
[2,2,1,1,1]
 => [[2,2,1,1,1],[]]
 => 16
[2,1,1,1,1,1]
 => [[2,1,1,1,1,1],[]]
 => 13
[1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1],[]]
 => 8
[8]
 => [[8],[]]
 => ? = 9
[7,1]
 => [[7,1],[]]
 => ? = 15
[6,2]
 => [[6,2],[]]
 => ? = 19
[6,1,1]
 => [[6,1,1],[]]
 => ? = 19
[5,3]
 => [[5,3],[]]
 => ? = 21
[5,2,1]
 => [[5,2,1],[]]
 => ? = 25
[5,1,1,1]
 => [[5,1,1,1],[]]
 => ? = 21
[4,4]
 => [[4,4],[]]
 => ? = 21
[4,3,1]
 => [[4,3,1],[]]
 => ? = 27
[4,2,2]
 => [[4,2,2],[]]
 => ? = 27
[4,2,1,1]
 => [[4,2,1,1],[]]
 => ? = 27
[4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ? = 21
[3,3,2]
 => [[3,3,2],[]]
 => ? = 27
[3,3,1,1]
 => [[3,3,1,1],[]]
 => ? = 27
[3,2,2,1]
 => [[3,2,2,1],[]]
 => ? = 27
[3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 25
[3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ? = 19
[2,2,2,2]
 => [[2,2,2,2],[]]
 => ? = 21
[2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 21
[2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 19
[2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 15
[1,1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1,1],[]]
 => ? = 9
[9]
 => [[9],[]]
 => ? = 10
[8,1]
 => [[8,1],[]]
 => ? = 17
[7,2]
 => [[7,2],[]]
 => ? = 22
[7,1,1]
 => [[7,1,1],[]]
 => ? = 22
[6,3]
 => [[6,3],[]]
 => ? = 25
[6,2,1]
 => [[6,2,1],[]]
 => ? = 30
[6,1,1,1]
 => [[6,1,1,1],[]]
 => ? = 25
[5,4]
 => [[5,4],[]]
 => ? = 26
[5,3,1]
 => [[5,3,1],[]]
 => ? = 34
[5,2,2]
 => [[5,2,2],[]]
 => ? = 34
[5,2,1,1]
 => [[5,2,1,1],[]]
 => ? = 34
[5,1,1,1,1]
 => [[5,1,1,1,1],[]]
 => ? = 26
[4,4,1]
 => [[4,4,1],[]]
 => ? = 34
[4,3,2]
 => [[4,3,2],[]]
 => ? = 37
[4,3,1,1]
 => [[4,3,1,1],[]]
 => ? = 37
[4,2,2,1]
 => [[4,2,2,1],[]]
 => ? = 37
[4,2,1,1,1]
 => [[4,2,1,1,1],[]]
 => ? = 34
[4,1,1,1,1,1]
 => [[4,1,1,1,1,1],[]]
 => ? = 25
[3,3,3]
 => [[3,3,3],[]]
 => ? = 34
[3,3,2,1]
 => [[3,3,2,1],[]]
 => ? = 37
[3,3,1,1,1]
 => [[3,3,1,1,1],[]]
 => ? = 34
[3,2,2,2]
 => [[3,2,2,2],[]]
 => ? = 34
[3,2,2,1,1]
 => [[3,2,2,1,1],[]]
 => ? = 34
[3,2,1,1,1,1]
 => [[3,2,1,1,1,1],[]]
 => ? = 30
[3,1,1,1,1,1,1]
 => [[3,1,1,1,1,1,1],[]]
 => ? = 22
[2,2,2,2,1]
 => [[2,2,2,2,1],[]]
 => ? = 26
[2,2,2,1,1,1]
 => [[2,2,2,1,1,1],[]]
 => ? = 25
[2,2,1,1,1,1,1]
 => [[2,2,1,1,1,1,1],[]]
 => ? = 22
Description
The total number of rook placements on a Ferrers board.