Processing math: 100%

Identifier
Values
[[1],[]] => ([],1) => [1] => 1
[[2],[]] => ([(0,1)],2) => [1] => 1
[[1,1],[]] => ([(0,1)],2) => [1] => 1
[[2,1],[1]] => ([],2) => [2] => 2
[[3],[]] => ([(0,2),(2,1)],3) => [1] => 1
[[2,1],[]] => ([(0,1),(0,2)],3) => [2] => 2
[[3,1],[1]] => ([(1,2)],3) => [3] => 3
[[2,2],[1]] => ([(0,2),(1,2)],3) => [2] => 2
[[3,2],[2]] => ([(1,2)],3) => [3] => 3
[[1,1,1],[]] => ([(0,2),(2,1)],3) => [1] => 1
[[2,2,1],[1,1]] => ([(1,2)],3) => [3] => 3
[[2,1,1],[1]] => ([(1,2)],3) => [3] => 3
[[3,2,1],[2,1]] => ([],3) => [3,3] => 6
[[4],[]] => ([(0,3),(2,1),(3,2)],4) => [1] => 1
[[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => [3] => 3
[[4,1],[1]] => ([(1,2),(2,3)],4) => [4] => 4
[[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => [2] => 2
[[3,2],[1]] => ([(0,3),(1,2),(1,3)],4) => [3,2] => 4
[[4,2],[2]] => ([(0,3),(1,2)],4) => [4,2] => 6
[[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => [3] => 3
[[3,2,1],[1,1]] => ([(1,2),(1,3)],4) => [8] => 8
[[3,1,1],[1]] => ([(0,3),(1,2)],4) => [4,2] => 6
[[4,2,1],[2,1]] => ([(2,3)],4) => [4,4,4] => 24
[[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => [3] => 3
[[4,3],[3]] => ([(1,2),(2,3)],4) => [4] => 4
[[2,2,1],[1]] => ([(0,3),(1,2),(1,3)],4) => [3,2] => 4
[[3,3,1],[2,1]] => ([(1,3),(2,3)],4) => [8] => 8
[[3,2,1],[2]] => ([(1,2),(1,3)],4) => [8] => 8
[[4,3,1],[3,1]] => ([(2,3)],4) => [4,4,4] => 24
[[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => [3] => 3
[[3,3,2],[2,2]] => ([(0,3),(1,2)],4) => [4,2] => 6
[[3,2,2],[2,1]] => ([(1,3),(2,3)],4) => [8] => 8
[[4,3,2],[3,2]] => ([(2,3)],4) => [4,4,4] => 24
[[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => [1] => 1
[[2,2,2,1],[1,1,1]] => ([(1,2),(2,3)],4) => [4] => 4
[[2,2,1,1],[1,1]] => ([(0,3),(1,2)],4) => [4,2] => 6
[[3,3,2,1],[2,2,1]] => ([(2,3)],4) => [4,4,4] => 24
[[2,1,1,1],[1]] => ([(1,2),(2,3)],4) => [4] => 4
[[3,2,2,1],[2,1,1]] => ([(2,3)],4) => [4,4,4] => 24
[[3,2,1,1],[2,1]] => ([(2,3)],4) => [4,4,4] => 24
[[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [1] => 1
[[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => [4] => 4
[[5,1],[1]] => ([(1,4),(3,2),(4,3)],5) => [5] => 5
[[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => 4
[[4,2],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => [5,4] => 16
[[5,2],[2]] => ([(0,3),(1,4),(4,2)],5) => [5,5] => 20
[[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => [4,2] => 6
[[4,2,1],[1,1]] => ([(1,3),(1,4),(4,2)],5) => [15] => 15
[[4,1,1],[1]] => ([(0,3),(1,4),(4,2)],5) => [5,5] => 20
[[3,3],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => 4
[[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => [5,4] => 16
[[5,3],[3]] => ([(0,3),(1,4),(4,2)],5) => [5,5] => 20
[[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => 4
[[3,3,1],[1,1]] => ([(1,2),(1,3),(2,4),(3,4)],5) => [5,5] => 20
[[3,2,1],[1]] => ([(0,3),(0,4),(1,2),(1,4)],5) => [12,4] => 44
[[3,2,2],[1,1]] => ([(0,4),(1,2),(1,3),(3,4)],5) => [4,4,3] => 18
[[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => [4] => 4
[[3,2,2,1],[1,1,1]] => ([(1,3),(1,4),(4,2)],5) => [15] => 15
[[3,1,1,1],[1]] => ([(0,3),(1,4),(4,2)],5) => [5,5] => 20
[[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 4
[[5,4],[4]] => ([(1,4),(3,2),(4,3)],5) => [5] => 5
[[3,3,1],[2]] => ([(0,4),(1,2),(1,3),(3,4)],5) => [4,4,3] => 18
[[4,4,1],[3,1]] => ([(1,4),(2,3),(3,4)],5) => [15] => 15
[[4,3,1],[3]] => ([(1,3),(1,4),(4,2)],5) => [15] => 15
[[2,2,2],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => 4
[[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [12,4] => 44
[[3,2,2],[2]] => ([(1,2),(1,3),(2,4),(3,4)],5) => [5,5] => 20
[[2,2,1,1],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => [5,4] => 16
[[3,2,1,1],[2]] => ([(1,3),(1,4),(4,2)],5) => [15] => 15
[[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => 6
[[4,4,3],[3,3]] => ([(0,3),(1,4),(4,2)],5) => [5,5] => 20
[[4,3,3],[3,2]] => ([(1,4),(2,3),(3,4)],5) => [15] => 15
[[2,2,2,1],[1,1]] => ([(0,3),(1,2),(1,4),(3,4)],5) => [5,4] => 16
[[3,3,3,1],[2,2,1]] => ([(1,4),(2,3),(3,4)],5) => [15] => 15
[[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 4
[[3,3,3,2],[2,2,2]] => ([(0,3),(1,4),(4,2)],5) => [5,5] => 20
[[3,2,2,2],[2,1,1]] => ([(1,4),(2,3),(3,4)],5) => [15] => 15
[[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [1] => 1
[[2,2,2,2,1],[1,1,1,1]] => ([(1,4),(3,2),(4,3)],5) => [5] => 5
[[2,2,2,1,1],[1,1,1]] => ([(0,3),(1,4),(4,2)],5) => [5,5] => 20
[[2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(4,2)],5) => [5,5] => 20
[[2,1,1,1,1],[1]] => ([(1,4),(3,2),(4,3)],5) => [5] => 5
[[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => 1
[[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => [5] => 5
[[6,1],[1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => [6] => 6
[[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => [5,4] => 16
[[5,2],[1]] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => [6,5,3] => 48
[[6,2],[2]] => ([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 60
[[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => [5,5] => 20
[[5,1,1],[1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 60
[[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => 4
[[4,3],[1]] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => [8,4,2] => 36
[[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => [12,4] => 44
[[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => [5,5] => 20
[[4,4],[2]] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => [5,4] => 16
[[5,4],[3]] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => [6,5,3] => 48
[[6,4],[4]] => ([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 60
[[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => 4
[[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => [5,4] => 16
[[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => [5] => 5
[[3,1,1,1,1],[1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 60
>>> Load all 140 entries. <<<
[[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => 5
[[6,5],[5]] => ([(1,5),(3,4),(4,2),(5,3)],6) => [6] => 6
[[3,3,3],[2,1]] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => [12,4] => 44
[[2,2,2,1],[1]] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => [8,4,2] => 36
[[2,2,1,1,1],[1]] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => [6,5,3] => 48
[[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => 20
[[5,5,4],[4,4]] => ([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 60
[[2,2,2,2],[1,1]] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => [5,4] => 16
[[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => 20
[[2,2,2,2,1],[1,1,1]] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => [6,5,3] => 48
[[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => 5
[[3,3,3,3,2],[2,2,2,2]] => ([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 60
[[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => 1
[[2,2,2,2,2,1],[1,1,1,1,1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => [6] => 6
[[2,2,2,2,1,1],[1,1,1,1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 60
[[2,2,1,1,1,1],[1,1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 60
[[2,1,1,1,1,1],[1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => [6] => 6
[[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => 1
[[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => [6] => 6
[[7,1],[1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => [7] => 7
[[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => [6,5,3] => 48
[[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => [6,6,3] => 60
[[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => [8,4,2] => 36
[[4,4],[1]] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => [8,4,2] => 36
[[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => [6,6,3] => 60
[[5,5],[3]] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => [6,5,3] => 48
[[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => [8,4,2] => 36
[[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => [6,5,3] => 48
[[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => [6] => 6
[[6,6],[5]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => 6
[[7,6],[6]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => [7] => 7
[[2,2,2,2],[1]] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => [8,4,2] => 36
[[5,5,5],[4,4]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [6,6,3] => 60
[[2,2,2,2,2],[1,1,1]] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => [6,5,3] => 48
[[3,3,3,3,3],[2,2,2,2]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [6,6,3] => 60
[[2,2,2,2,2,2],[1,1,1,1,1]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => 6
[[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => 1
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => [7] => 7
[[2,1,1,1,1,1,1],[1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => [7] => 7
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Description
The number of ways to place as many non-attacking rooks as possible on a Ferrers board.
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell d is greater than a cell c if the entry in d must be larger than the entry of c in any standard Young tableau on the skew partition.