Identifier
Values
[] => ([],1) => ([],1) => 0
[[]] => ([(0,1)],2) => ([],2) => 1
[[[]]] => ([(0,2),(2,1)],3) => ([],3) => 1
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 2
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => 1
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => 1
[[[[]]]] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => ([(2,3),(2,4),(3,4)],5) => 2
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 1
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => 1
[[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([(3,4),(3,5),(4,5)],6) => 2
[[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 1
[[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => 1
[[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The Colin de Verdière graph invariant.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
incomparability graph
Description
The incomparability graph of a poset.