Identifier
Values
[] => ([],1) => [1] => 1
[[]] => ([(0,1)],2) => [1] => 1
[[],[]] => ([(0,2),(1,2)],3) => [2] => 2
[[[]]] => ([(0,2),(2,1)],3) => [1] => 1
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => [3,3] => 6
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => [3] => 3
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => [3] => 3
[[[],[]]] => ([(0,3),(1,3),(3,2)],4) => [2] => 2
[[[[]]]] => ([(0,3),(2,1),(3,2)],4) => [1] => 1
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => 24
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => 24
[[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => [8] => 8
[[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 4
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => 24
[[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => 6
[[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => [8] => 8
[[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 4
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => 6
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 3
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 3
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => [2] => 2
[[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [1] => 1
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 15
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 15
[[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => 20
[[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => 5
[[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => 20
[[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => 20
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 15
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 15
[[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => 20
[[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => 5
[[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => 24
[[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => 24
[[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => [8] => 8
[[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => 4
[[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => 24
[[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => 6
[[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => [8] => 8
[[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => 4
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => 6
[[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => 3
[[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => 3
[[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => 2
[[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => 1
[[],[[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [12] => 12
[[],[[[[[]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => 6
[[[]],[[[[]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [6,6,3] => 60
[[[[[]]]],[[]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [6,6,3] => 60
[[[[[],[]]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [12] => 12
[[[[[[]]]]],[]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => 6
[[[],[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [15] => 15
[[[],[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [15] => 15
[[[],[[[],[]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => [5,5] => 20
[[[],[[[[]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => 5
[[[[]],[[[]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [5,5] => 20
[[[[[]]],[[]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [5,5] => 20
[[[[],[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [15] => 15
[[[[[]],[]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [15] => 15
[[[[[],[]]],[]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => [5,5] => 20
[[[[[[]]]],[]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => 5
[[[[],[],[[]]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => 24
[[[[],[[]],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => 24
[[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => [8] => 8
[[[[],[[[]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => 4
[[[[[]],[],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => 24
[[[[[]],[[]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [4,2] => 6
[[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => [8] => 8
[[[[[[]]],[]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => 4
[[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [3,3] => 6
[[[[[],[[]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => 3
[[[[[[]],[]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => 3
[[[[[[],[]]]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [2] => 2
[[[[[[[]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => 1
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Description
The number of ways to place as many non-attacking rooks as possible on a Ferrers board.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.