- FindStat

Identifier

Mp00047: Ordered trees —to poset⟶ Posets
St000080: Posets ⟶ ℤ (values match St000528The height of a poset.)

Values

[] => ([],1) => 0
[[]] => ([(0,1)],2) => 1
[[],[]] => ([(0,2),(1,2)],3) => 1
[[[]]] => ([(0,2),(2,1)],3) => 2
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 1
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => 2
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => 2
[[[],[]]] => ([(0,3),(1,3),(3,2)],4) => 2
[[[[]]]] => ([(0,3),(2,1),(3,2)],4) => 3
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 2
[[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 2
[[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 2
[[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => 2
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => 3
[[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 2
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 4
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 3
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 3
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 2
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 3
[[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 3
[[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 4
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 2
[[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 3
[[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 3
[[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3
[[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 4
[[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 3
[[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 3
[[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3
[[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 4
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 3
[[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 4
[[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 4
[[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 4
[[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5

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

click to show known generating functions

$F_{1} = 1$

$F_{2} = q$

$F_{3} = q + q^{2}$

$F_{4} = q + 3\ q^{2} + q^{3}$

$F_{5} = q + 7\ q^{2} + 5\ q^{3} + q^{4}$

$F_{6} = q + 15\ q^{2} + 18\ q^{3} + 7\ q^{4} + q^{5}$

Description

The rank of the poset.

Map

to poset

Description

Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.