Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001659
(load all 3 compositions to match this statistic)
Mapping
St001659: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 2
[3]
 => 3
[2,1]
 => 1
[1,1,1]
 => 3
[4]
 => 4
[3,1]
 => 2
[2,2]
 => 2
[2,1,1]
 => 2
[1,1,1,1]
 => 4
[5]
 => 5
[4,1]
 => 3
[3,2]
 => 4
[3,1,1]
 => 4
[2,2,1]
 => 4
[2,1,1,1]
 => 3
[1,1,1,1,1]
 => 5
[6]
 => 6
[5,1]
 => 4
[4,2]
 => 6
[4,1,1]
 => 6
[3,3]
 => 6
[3,2,1]
 => 1
[3,1,1,1]
 => 6
[2,2,2]
 => 6
[2,2,1,1]
 => 6
[2,1,1,1,1]
 => 4
[1,1,1,1,1,1]
 => 6
[7]
 => 7
[6,1]
 => 5
[5,2]
 => 8
[5,1,1]
 => 8
[4,3]
 => 9
[4,2,1]
 => 2
[4,1,1,1]
 => 9
[3,3,1]
 => 2
[3,2,2]
 => 2
[3,2,1,1]
 => 2
[3,1,1,1,1]
 => 8
[2,2,2,1]
 => 9
[2,2,1,1,1]
 => 8
[2,1,1,1,1,1]
 => 5
[1,1,1,1,1,1,1]
 => 7
[8]
 => 8
[7,1]
 => 6
[6,2]
 => 10
[6,1,1]
 => 10
[5,3]
 => 12
[5,2,1]
 => 3
Description
The number of ways to place as many non-attacking rooks as possible on a Ferrers board.
Matching statistic: St000531
Mapping
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000531: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 34%
Values
[1]
 => [[1],[]]
 => ([],1)
 => [1]
 => 1
[2]
 => [[2],[]]
 => ([(0,1)],2)
 => [2]
 => 2
[1,1]
 => [[1,1],[]]
 => ([(0,1)],2)
 => [2]
 => 2
[3]
 => [[3],[]]
 => ([(0,2),(2,1)],3)
 => [3]
 => 3
[2,1]
 => [[2,1],[]]
 => ([(0,1),(0,2)],3)
 => [2,1]
 => 1
[1,1,1]
 => [[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => [3]
 => 3
[4]
 => [[4],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => [4]
 => 4
[3,1]
 => [[3,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => [3,1]
 => 2
[2,2]
 => [[2,2],[]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => [3,1]
 => 2
[2,1,1]
 => [[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => [3,1]
 => 2
[1,1,1,1]
 => [[1,1,1,1],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => [4]
 => 4
[5]
 => [[5],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => [5]
 => 5
[4,1]
 => [[4,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => [4,1]
 => 3
[3,2]
 => [[3,2],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => 4
[3,1,1]
 => [[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => [3,2]
 => 4
[2,2,1]
 => [[2,2,1],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => 4
[2,1,1,1]
 => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => [4,1]
 => 3
[1,1,1,1,1]
 => [[1,1,1,1,1],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => [5]
 => 5
[6]
 => [[6],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [6]
 => 6
[5,1]
 => [[5,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5,1]
 => 4
[4,2]
 => [[4,2],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => [4,2]
 => 6
[4,1,1]
 => [[4,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => [4,2]
 => 6
[3,3]
 => [[3,3],[]]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [4,2]
 => 6
[3,2,1]
 => [[3,2,1],[]]
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => [3,2,1]
 => 1
[3,1,1,1]
 => [[3,1,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => [4,2]
 => 6
[2,2,2]
 => [[2,2,2],[]]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [4,2]
 => 6
[2,2,1,1]
 => [[2,2,1,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => [4,2]
 => 6
[2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5,1]
 => 4
[1,1,1,1,1,1]
 => [[1,1,1,1,1,1],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [6]
 => 6
[7]
 => [[7],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => [7]
 => 7
[6,1]
 => [[6,1],[]]
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => [6,1]
 => 5
[5,2]
 => [[5,2],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
 => [5,2]
 => 8
[5,1,1]
 => [[5,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => [5,2]
 => 8
[4,3]
 => [[4,3],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
 => [4,3]
 => 9
[4,2,1]
 => [[4,2,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
 => [4,2,1]
 => 2
[4,1,1,1]
 => [[4,1,1,1],[]]
 => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => [4,3]
 => 9
[3,3,1]
 => [[3,3,1],[]]
 => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
 => [4,2,1]
 => 2
[3,2,2]
 => [[3,2,2],[]]
 => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
 => [4,2,1]
 => 2
[3,2,1,1]
 => [[3,2,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
 => [4,2,1]
 => 2
[3,1,1,1,1]
 => [[3,1,1,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => [5,2]
 => 8
[2,2,2,1]
 => [[2,2,2,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
 => [4,3]
 => 9
[2,2,1,1,1]
 => [[2,2,1,1,1],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
 => [5,2]
 => 8
[2,1,1,1,1,1]
 => [[2,1,1,1,1,1],[]]
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => [6,1]
 => 5
[1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => [7]
 => 7
[8]
 => [[8],[]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => [8]
 => 8
[7,1]
 => [[7,1],[]]
 => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
 => [7,1]
 => 6
[6,2]
 => [[6,2],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
 => [6,2]
 => 10
[6,1,1]
 => [[6,1,1],[]]
 => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
 => [6,2]
 => 10
[5,3]
 => [[5,3],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
 => [5,3]
 => 12
[5,2,1]
 => [[5,2,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
 => [5,2,1]
 => 3
[11]
 => [[11],[]]
 => ?
 => ?
 => ? = 11
[10,1]
 => [[10,1],[]]
 => ?
 => ?
 => ? = 9
[9,2]
 => [[9,2],[]]
 => ?
 => ?
 => ? = 16
[9,1,1]
 => [[9,1,1],[]]
 => ?
 => ?
 => ? = 16
[8,3]
 => [[8,3],[]]
 => ?
 => ?
 => ? = 21
[8,2,1]
 => [[8,2,1],[]]
 => ?
 => ?
 => ? = 6
[8,1,1,1]
 => [[8,1,1,1],[]]
 => ?
 => ?
 => ? = 21
[7,4]
 => [[7,4],[]]
 => ?
 => ?
 => ? = 24
[7,3,1]
 => [[7,3,1],[]]
 => ?
 => ?
 => ? = 10
[7,2,2]
 => [[7,2,2],[]]
 => ?
 => ?
 => ? = 10
[7,2,1,1]
 => [[7,2,1,1],[]]
 => ?
 => ?
 => ? = 10
[7,1,1,1,1]
 => [[7,1,1,1,1],[]]
 => ?
 => ?
 => ? = 24
[6,5]
 => [[6,5],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(3,9),(4,3),(4,10),(5,1),(5,8),(6,4),(6,7),(7,10),(9,8),(10,9)],11)
 => ?
 => ? = 25
[6,4,1]
 => [[6,4,1],[]]
 => ?
 => ?
 => ? = 12
[6,3,2]
 => [[6,3,2],[]]
 => ?
 => ?
 => ? = 16
[6,3,1,1]
 => [[6,3,1,1],[]]
 => ?
 => ?
 => ? = 16
[6,2,2,1]
 => [[6,2,2,1],[]]
 => ?
 => ?
 => ? = 16
[6,2,1,1,1]
 => [[6,2,1,1,1],[]]
 => ?
 => ?
 => ? = 12
[6,1,1,1,1,1]
 => [[6,1,1,1,1,1],[]]
 => ?
 => ?
 => ? = 25
[5,5,1]
 => [[5,5,1],[]]
 => ([(0,5),(0,6),(2,8),(3,2),(3,9),(4,3),(4,10),(5,4),(5,7),(6,1),(6,7),(7,10),(9,8),(10,9)],11)
 => ?
 => ? = 12
[5,4,2]
 => [[5,4,2],[]]
 => ([(0,5),(0,6),(2,9),(3,4),(3,10),(4,1),(4,8),(5,3),(5,7),(6,2),(6,7),(7,9),(7,10),(10,8)],11)
 => ?
 => ? = 18
[5,4,1,1]
 => [[5,4,1,1],[]]
 => ([(0,6),(0,7),(3,2),(4,5),(4,10),(5,1),(5,9),(6,4),(6,8),(7,3),(7,8),(8,10),(10,9)],11)
 => ?
 => ? = 18
[5,3,3]
 => [[5,3,3],[]]
 => ([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
 => ?
 => ? = 18
[5,3,2,1]
 => [[5,3,2,1],[]]
 => ([(0,6),(0,7),(3,2),(4,3),(4,9),(5,1),(5,10),(6,4),(6,8),(7,5),(7,8),(8,9),(8,10)],11)
 => ?
 => ? = 2
[5,3,1,1,1]
 => [[5,3,1,1,1],[]]
 => ([(0,7),(0,8),(3,5),(4,6),(4,10),(5,1),(6,2),(7,3),(7,9),(8,4),(8,9),(9,10)],11)
 => ?
 => ? = 18
[5,2,2,2]
 => [[5,2,2,2],[]]
 => ([(0,6),(0,7),(2,9),(3,4),(4,1),(5,2),(5,10),(6,3),(6,8),(7,5),(7,8),(8,10),(10,9)],11)
 => ?
 => ? = 18
[5,2,2,1,1]
 => [[5,2,2,1,1],[]]
 => ([(0,7),(0,8),(3,5),(4,6),(4,10),(5,1),(6,2),(7,3),(7,9),(8,4),(8,9),(9,10)],11)
 => ?
 => ? = 18
[5,2,1,1,1,1]
 => [[5,2,1,1,1,1],[]]
 => ?
 => ?
 => ? = 12
[5,1,1,1,1,1,1]
 => [[5,1,1,1,1,1,1],[]]
 => ?
 => ?
 => ? = 24
[4,4,2,1]
 => [[4,4,2,1],[]]
 => ([(0,5),(0,6),(2,8),(3,2),(3,10),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(7,10),(10,8)],11)
 => ?
 => ? = 2
[4,4,1,1,1]
 => [[4,4,1,1,1],[]]
 => ([(0,6),(0,7),(2,9),(3,4),(4,1),(5,2),(5,10),(6,3),(6,8),(7,5),(7,8),(8,10),(10,9)],11)
 => ?
 => ? = 18
[4,3,3,1]
 => [[4,3,3,1],[]]
 => ([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
 => ?
 => ? = 2
[4,3,2,2]
 => [[4,3,2,2],[]]
 => ([(0,5),(0,6),(2,8),(3,2),(3,10),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(7,10),(10,8)],11)
 => ?
 => ? = 2
[4,3,2,1,1]
 => [[4,3,2,1,1],[]]
 => ([(0,6),(0,7),(3,2),(4,3),(4,9),(5,1),(5,10),(6,4),(6,8),(7,5),(7,8),(8,9),(8,10)],11)
 => ?
 => ? = 2
[4,3,1,1,1,1]
 => [[4,3,1,1,1,1],[]]
 => ?
 => ?
 => ? = 16
[4,2,2,2,1]
 => [[4,2,2,2,1],[]]
 => ([(0,6),(0,7),(3,2),(4,5),(4,10),(5,1),(5,9),(6,4),(6,8),(7,3),(7,8),(8,10),(10,9)],11)
 => ?
 => ? = 18
[4,2,2,1,1,1]
 => [[4,2,2,1,1,1],[]]
 => ?
 => ?
 => ? = 16
[4,2,1,1,1,1,1]
 => [[4,2,1,1,1,1,1],[]]
 => ?
 => ?
 => ? = 10
[4,1,1,1,1,1,1,1]
 => [[4,1,1,1,1,1,1,1],[]]
 => ?
 => ?
 => ? = 21
[3,3,3,1,1]
 => [[3,3,3,1,1],[]]
 => ([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
 => ?
 => ? = 18
[3,3,2,2,1]
 => [[3,3,2,2,1],[]]
 => ([(0,5),(0,6),(2,9),(3,4),(3,10),(4,1),(4,8),(5,3),(5,7),(6,2),(6,7),(7,9),(7,10),(10,8)],11)
 => ?
 => ? = 18
[3,3,2,1,1,1]
 => [[3,3,2,1,1,1],[]]
 => ?
 => ?
 => ? = 16
[3,3,1,1,1,1,1]
 => [[3,3,1,1,1,1,1],[]]
 => ?
 => ?
 => ? = 10
[3,2,2,2,2]
 => [[3,2,2,2,2],[]]
 => ([(0,5),(0,6),(2,8),(3,2),(3,9),(4,3),(4,10),(5,4),(5,7),(6,1),(6,7),(7,10),(9,8),(10,9)],11)
 => ?
 => ? = 12
[3,2,2,2,1,1]
 => [[3,2,2,2,1,1],[]]
 => ?
 => ?
 => ? = 12
[3,2,2,1,1,1,1]
 => [[3,2,2,1,1,1,1],[]]
 => ?
 => ?
 => ? = 10
[3,2,1,1,1,1,1,1]
 => [[3,2,1,1,1,1,1,1],[]]
 => ?
 => ?
 => ? = 6
[3,1,1,1,1,1,1,1,1]
 => [[3,1,1,1,1,1,1,1,1],[]]
 => ?
 => ?
 => ? = 16
[2,2,2,2,2,1]
 => [[2,2,2,2,2,1],[]]
 => ?
 => ?
 => ? = 25
[2,2,2,2,1,1,1]
 => [[2,2,2,2,1,1,1],[]]
 => ?
 => ?
 => ? = 24
Description
The leading coefficient of the rook polynomial of an integer partition. Let $m$ be the minimum of the number of parts and the size of the first part of an integer partition $\lambda$. Then this statistic yields the number of ways to place $m$ non-attacking rooks on the Ferrers board of $\lambda$.
Matching statistic: St001660
(load all 4 compositions to match this statistic)
Mapping
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001660: Skew partitions ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 17%
Values
[1]
 => [[1],[]]
 => 1
[2]
 => [[2],[]]
 => 2
[1,1]
 => [[1,1],[]]
 => 2
[3]
 => [[3],[]]
 => 3
[2,1]
 => [[2,1],[]]
 => 1
[1,1,1]
 => [[1,1,1],[]]
 => 3
[4]
 => [[4],[]]
 => 4
[3,1]
 => [[3,1],[]]
 => 2
[2,2]
 => [[2,2],[]]
 => 2
[2,1,1]
 => [[2,1,1],[]]
 => 2
[1,1,1,1]
 => [[1,1,1,1],[]]
 => 4
[5]
 => [[5],[]]
 => 5
[4,1]
 => [[4,1],[]]
 => 3
[3,2]
 => [[3,2],[]]
 => 4
[3,1,1]
 => [[3,1,1],[]]
 => 4
[2,2,1]
 => [[2,2,1],[]]
 => 4
[2,1,1,1]
 => [[2,1,1,1],[]]
 => 3
[1,1,1,1,1]
 => [[1,1,1,1,1],[]]
 => 5
[6]
 => [[6],[]]
 => 6
[5,1]
 => [[5,1],[]]
 => 4
[4,2]
 => [[4,2],[]]
 => 6
[4,1,1]
 => [[4,1,1],[]]
 => 6
[3,3]
 => [[3,3],[]]
 => 6
[3,2,1]
 => [[3,2,1],[]]
 => 1
[3,1,1,1]
 => [[3,1,1,1],[]]
 => 6
[2,2,2]
 => [[2,2,2],[]]
 => 6
[2,2,1,1]
 => [[2,2,1,1],[]]
 => 6
[2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => 4
[1,1,1,1,1,1]
 => [[1,1,1,1,1,1],[]]
 => 6
[7]
 => [[7],[]]
 => 7
[6,1]
 => [[6,1],[]]
 => 5
[5,2]
 => [[5,2],[]]
 => 8
[5,1,1]
 => [[5,1,1],[]]
 => 8
[4,3]
 => [[4,3],[]]
 => 9
[4,2,1]
 => [[4,2,1],[]]
 => 2
[4,1,1,1]
 => [[4,1,1,1],[]]
 => 9
[3,3,1]
 => [[3,3,1],[]]
 => 2
[3,2,2]
 => [[3,2,2],[]]
 => 2
[3,2,1,1]
 => [[3,2,1,1],[]]
 => 2
[3,1,1,1,1]
 => [[3,1,1,1,1],[]]
 => 8
[2,2,2,1]
 => [[2,2,2,1],[]]
 => 9
[2,2,1,1,1]
 => [[2,2,1,1,1],[]]
 => 8
[2,1,1,1,1,1]
 => [[2,1,1,1,1,1],[]]
 => 5
[1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1],[]]
 => 7
[8]
 => [[8],[]]
 => ? = 8
[7,1]
 => [[7,1],[]]
 => ? = 6
[6,2]
 => [[6,2],[]]
 => ? = 10
[6,1,1]
 => [[6,1,1],[]]
 => ? = 10
[5,3]
 => [[5,3],[]]
 => ? = 12
[5,2,1]
 => [[5,2,1],[]]
 => ? = 3
[5,1,1,1]
 => [[5,1,1,1],[]]
 => ? = 12
[4,4]
 => [[4,4],[]]
 => ? = 12
[4,3,1]
 => [[4,3,1],[]]
 => ? = 4
[4,2,2]
 => [[4,2,2],[]]
 => ? = 4
[4,2,1,1]
 => [[4,2,1,1],[]]
 => ? = 4
[4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ? = 12
[3,3,2]
 => [[3,3,2],[]]
 => ? = 4
[3,3,1,1]
 => [[3,3,1,1],[]]
 => ? = 4
[3,2,2,1]
 => [[3,2,2,1],[]]
 => ? = 4
[3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 3
[3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ? = 10
[2,2,2,2]
 => [[2,2,2,2],[]]
 => ? = 12
[2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 12
[2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 10
[2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 6
[1,1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1,1],[]]
 => ? = 8
[9]
 => [[9],[]]
 => ? = 9
[8,1]
 => [[8,1],[]]
 => ? = 7
[7,2]
 => [[7,2],[]]
 => ? = 12
[7,1,1]
 => [[7,1,1],[]]
 => ? = 12
[6,3]
 => [[6,3],[]]
 => ? = 15
[6,2,1]
 => [[6,2,1],[]]
 => ? = 4
[6,1,1,1]
 => [[6,1,1,1],[]]
 => ? = 15
[5,4]
 => [[5,4],[]]
 => ? = 16
[5,3,1]
 => [[5,3,1],[]]
 => ? = 6
[5,2,2]
 => [[5,2,2],[]]
 => ? = 6
[5,2,1,1]
 => [[5,2,1,1],[]]
 => ? = 6
[5,1,1,1,1]
 => [[5,1,1,1,1],[]]
 => ? = 16
[4,4,1]
 => [[4,4,1],[]]
 => ? = 6
[4,3,2]
 => [[4,3,2],[]]
 => ? = 8
[4,3,1,1]
 => [[4,3,1,1],[]]
 => ? = 8
[4,2,2,1]
 => [[4,2,2,1],[]]
 => ? = 8
[4,2,1,1,1]
 => [[4,2,1,1,1],[]]
 => ? = 6
[4,1,1,1,1,1]
 => [[4,1,1,1,1,1],[]]
 => ? = 15
[3,3,3]
 => [[3,3,3],[]]
 => ? = 6
[3,3,2,1]
 => [[3,3,2,1],[]]
 => ? = 8
[3,3,1,1,1]
 => [[3,3,1,1,1],[]]
 => ? = 6
[3,2,2,2]
 => [[3,2,2,2],[]]
 => ? = 6
[3,2,2,1,1]
 => [[3,2,2,1,1],[]]
 => ? = 6
[3,2,1,1,1,1]
 => [[3,2,1,1,1,1],[]]
 => ? = 4
[3,1,1,1,1,1,1]
 => [[3,1,1,1,1,1,1],[]]
 => ? = 12
[2,2,2,2,1]
 => [[2,2,2,2,1],[]]
 => ? = 16
[2,2,2,1,1,1]
 => [[2,2,2,1,1,1],[]]
 => ? = 15
[2,2,1,1,1,1,1]
 => [[2,2,1,1,1,1,1],[]]
 => ? = 12
Description
The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board.