Identifier
Values
[] => ([],1) => ([],1) => 1
[[]] => ([(0,1)],2) => ([(0,1)],2) => 2
[[],[]] => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 3
[[[]]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 6
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 4
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => 8
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => 8
[[[],[]]] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(3,1),(3,2)],4) => 12
[[[[]]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 24
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => 5
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => 10
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => 10
[[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 15
[[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => 10
[[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,3),(0,4),(3,2),(4,1)],5) => 20
[[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 15
[[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => 30
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => ([(0,4),(4,1),(4,2),(4,3)],5) => 20
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => 40
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,3),(3,4),(4,1),(4,2)],5) => 60
[[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 120
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 6
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 12
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 12
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 18
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 36
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 12
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 24
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 18
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 36
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 24
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 48
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 48
[[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 72
[[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 144
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 12
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 24
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 24
[[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 36
[[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 72
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 18
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 36
[[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 36
[[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 72
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 24
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 48
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 48
[[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 72
[[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 144
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 30
[[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 60
[[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 60
[[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 90
[[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 60
[[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 120
[[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 90
[[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 180
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 120
[[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 240
[[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 360
[[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 720
[[],[],[],[],[],[]] => ([(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) => 7
[[],[],[],[],[[]]] => ([(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) => 14
[[],[],[],[[]],[]] => ([(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) => 14
[[],[],[],[[],[]]] => ([(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) => 21
[[],[],[],[[[]]]] => ([(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) => 42
[[],[],[[]],[],[]] => ([(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) => 14
[[],[],[[]],[[]]] => ([(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) => 28
[[],[],[[],[]],[]] => ([(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) => 21
[[],[],[[[]]],[]] => ([(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) => 42
[[],[],[[],[],[]]] => ([(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) => 28
[[],[],[[[],[]]]] => ([(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) => 84
[[],[[]],[],[],[]] => ([(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) => 14
[[],[[]],[],[[]]] => ([(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) => 28
[[],[[]],[[]],[]] => ([(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) => 28
[[],[[]],[[],[]]] => ([(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) => 42
[[],[[],[]],[],[]] => ([(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) => 21
[[],[[[]]],[],[]] => ([(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) => 42
[[],[[],[]],[[]]] => ([(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) => 42
[[],[[],[],[]],[]] => ([(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) => 28
[[],[[[],[]]],[]] => ([(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) => 84
[[],[[],[],[],[]]] => ([(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) => 35
[[[]],[],[],[],[]] => ([(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) => 14
[[[]],[],[],[[]]] => ([(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) => 28
[[[]],[],[[]],[]] => ([(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) => 28
[[[]],[],[[],[]]] => ([(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) => 42
[[[]],[[]],[],[]] => ([(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) => 28
[[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => 56
[[[]],[[],[]],[]] => ([(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) => 42
[[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => 56
[[[],[]],[],[],[]] => ([(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) => 21
[[[[]]],[],[],[]] => ([(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) => 42
[[[],[]],[],[[]]] => ([(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) => 42
[[[],[]],[[]],[]] => ([(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) => 42
[[[],[]],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => ([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => 63
[[[],[],[]],[],[]] => ([(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) => 28
[[[[],[]]],[],[]] => ([(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) => 84
>>> Load all 105 entries. <<<
[[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => 56
[[[],[],[],[]],[]] => ([(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) => 35
[[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 42
[[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 210
search for individual values
searching the database for the individual values of this statistic
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Description
The product of the sizes of the principal order filters 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 $y \leq x$.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.