Identifier
Values
[] => ([],1) => ([],1) => 0
[[]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[],[]] => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 2
[[[]]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 3
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => 2
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => 2
[[[],[]]] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(3,1),(3,2)],4) => 2
[[[[]]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => 4
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => 3
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => 3
[[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 2
[[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 2
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => 3
[[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,3),(0,4),(3,2),(4,1)],5) => 2
[[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 2
[[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 2
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => ([(0,4),(4,1),(4,2),(4,3)],5) => 3
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 2
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 2
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,3),(3,4),(4,1),(4,2)],5) => 2
[[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 5
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 4
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 4
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 3
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 3
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 4
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 3
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 3
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 3
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 3
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 2
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 2
[[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 2
[[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 2
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 4
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 3
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 3
[[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 2
[[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 2
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 3
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 3
[[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 2
[[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 2
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 3
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 2
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 2
[[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 2
[[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 2
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 4
[[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 3
[[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 3
[[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 2
[[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 2
[[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 3
[[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 2
[[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 2
[[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 2
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 3
[[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 2
[[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 2
[[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 2
[[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 6
[[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 5
[[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 5
[[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 4
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 4
[[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 5
[[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 4
[[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 4
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 4
[[],[],[[],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 3
[[],[],[[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => 3
[[],[],[[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => 3
[[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 3
[[],[],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7) => 3
[[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 5
[[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 4
[[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 4
[[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => 3
[[],[[]],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => 3
[[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 4
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 4
[[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => 3
[[],[[[]]],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => 3
[[],[[],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 3
[[],[[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => 3
[[],[[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => 3
[[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 3
[[],[[[[]]]],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7) => 3
[[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 4
[[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => 3
[[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => 3
[[],[[],[[],[]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7) => 2
[[],[[],[[[]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7) => 2
[[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => 3
[[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7) => 2
[[],[[[],[]],[]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7) => 2
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Description
The maximal number of elements covered by an element in a poset.
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
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