- FindStat

Identifier

Mp00328: Ordered trees —DeBruijn-Morselt plane tree automorphism⟶ Ordered trees
Mp00047: Ordered trees —to poset⟶ Posets
St000068: Posets ⟶ ℤ

Values

[] => [] => ([],1) => 1

[[]] => [[]] => ([(0,1)],2) => 1

[[],[]] => [[[]]] => ([(0,2),(2,1)],3) => 1

[[[]]] => [[],[]] => ([(0,2),(1,2)],3) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[],[],[],[],[],[]] => [[[[[[[]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[[],[],[],[],[[]]] => [[[[[[],[]]]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2

[[],[],[],[[]],[]] => [[[[[],[[]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2

[[],[],[],[[],[]]] => [[[[[[]],[]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2

[[],[],[],[[[]]]] => [[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 3

[[],[],[[]],[],[]] => [[[[],[[[]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2

[[],[],[[]],[[]]] => [[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3

[[],[],[[],[]],[]] => [[[[[]],[[]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2

[[],[],[[[]]],[]] => [[[[],[],[[]]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 3

[[],[],[[],[],[]]] => [[[[[[]]],[]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2

[[],[],[[],[[]]]] => [[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3

[[],[],[[[]],[]]] => [[[[],[[]],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 3

[[],[],[[[],[]]]] => [[[[[]],[],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 3

[[],[],[[[[]]]]] => [[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 4

[[],[[]],[],[],[]] => [[[],[[[[]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2

[[],[[]],[],[[]]] => [[[],[[[],[]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3

[[],[[]],[[]],[]] => [[[],[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3

[[],[[]],[[],[]]] => [[[],[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3

[[],[[]],[[[]]]] => [[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 4

[[],[[],[]],[],[]] => [[[[]],[[[]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2

[[],[[[]]],[],[]] => [[[],[],[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 3

[[],[[],[]],[[]]] => [[[[]],[[],[]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3

[[],[[[]]],[[]]] => [[[],[],[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 4

[[],[[],[],[]],[]] => [[[[[]]],[[]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2

[[],[[],[[]]],[]] => [[[[],[]],[[]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3

[[],[[[]],[]],[]] => [[[],[[]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3

[[],[[[],[]]],[]] => [[[[]],[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3

[[],[[[[]]]],[]] => [[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 4

[[],[[],[],[],[]]] => [[[[[[]]]],[]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2

[[],[[],[],[[]]]] => [[[[[],[]]],[]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3

[[],[[],[[]],[]]] => [[[[],[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3

[[],[[],[[],[]]]] => [[[[[]],[]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3

[[],[[],[[[]]]]] => [[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 4

[[],[[[]],[],[]]] => [[[],[[[]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 3

[[],[[[]],[[]]]] => [[[],[[],[]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 4

[[],[[[],[]],[]]] => [[[[]],[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3

>>> Load all 237 entries. <<<

[[],[[[[]]],[]]] => [[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 4

[[],[[[],[],[]]]] => [[[[[]]],[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 3

[[],[[[],[[]]]]] => [[[[],[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 4

[[],[[[[]],[]]]] => [[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 4

[[],[[[[],[]]]]] => [[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 4

[[],[[[[[]]]]]] => [[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 5

[[[]],[],[],[],[]] => [[],[[[[[]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2

[[[]],[],[],[[]]] => [[],[[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3

[[[]],[],[[]],[]] => [[],[[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3

[[[]],[],[[],[]]] => [[],[[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3

[[[]],[],[[[]]]] => [[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 4

[[[]],[[]],[],[]] => [[],[[],[[[]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3

[[[]],[[]],[[]]] => [[],[[],[[],[]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4

[[[]],[[],[]],[]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3

[[[]],[[[]]],[]] => [[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 4

[[[]],[[],[],[]]] => [[],[[[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3

[[[]],[[],[[]]]] => [[],[[[],[]],[]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4

[[[]],[[[]],[]]] => [[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 4

[[[]],[[[],[]]]] => [[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 4

[[[]],[[[[]]]]] => [[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 5

[[[],[]],[],[],[]] => [[[]],[[[[]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2

[[[[]]],[],[],[]] => [[],[],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 3

[[[],[]],[],[[]]] => [[[]],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3

[[[[]]],[],[[]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 4

[[[],[]],[[]],[]] => [[[]],[[],[[]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3

[[[[]]],[[]],[]] => [[],[],[[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 4

[[[],[]],[[],[]]] => [[[]],[[[]],[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3

[[[],[]],[[[]]]] => [[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 4

[[[[]]],[[],[]]] => [[],[],[[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 4

[[[[]]],[[[]]]] => [[],[],[[],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 5

[[[],[],[]],[],[]] => [[[[]]],[[[]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2

[[[],[[]]],[],[]] => [[[],[]],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3

[[[[]],[]],[],[]] => [[],[[]],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 3

[[[[],[]]],[],[]] => [[[]],[],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 3

[[[[[]]]],[],[]] => [[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4

[[[],[],[]],[[]]] => [[[[]]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3

[[[],[[]]],[[]]] => [[[],[]],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 4

[[[[]],[]],[[]]] => [[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[],[]]],[[]]] => [[[]],[],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[]]]],[[]]] => [[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5

[[[],[],[],[]],[]] => [[[[[]]]],[[]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2

[[[],[],[[]]],[]] => [[[[],[]]],[[]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3

[[[],[[]],[]],[]] => [[[],[[]]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3

[[[],[[],[]]],[]] => [[[[]],[]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3

[[[],[[[]]]],[]] => [[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 4

[[[[]],[],[]],[]] => [[],[[[]]],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 3

[[[[]],[[]]],[]] => [[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[],[]],[]],[]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3

[[[[[]]],[]],[]] => [[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[],[],[]]],[]] => [[[[]]],[],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 3

[[[[],[[]]]],[]] => [[[],[]],[],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[]],[]]],[]] => [[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[],[]]]],[]] => [[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[[]]]]],[]] => [[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5

[[[],[],[],[],[]]] => [[[[[[]]]]],[]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2

[[[],[],[],[[]]]] => [[[[[],[]]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3

[[[],[],[[]],[]]] => [[[[],[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3

[[[],[],[[],[]]]] => [[[[[]],[]]],[]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3

[[[],[],[[[]]]]] => [[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 4

[[[],[[]],[],[]]] => [[[],[[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3

[[[],[[]],[[]]]] => [[[],[[],[]]],[]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4

[[[],[[],[]],[]]] => [[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3

[[[],[[[]]],[]]] => [[[],[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 4

[[[],[[],[],[]]]] => [[[[[]]],[]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3

[[[],[[],[[]]]]] => [[[[],[]],[]],[]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4

[[[],[[[]],[]]]] => [[[],[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 4

[[[],[[[],[]]]]] => [[[[]],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 4

[[[],[[[[]]]]]] => [[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 5

[[[[]],[],[],[]]] => [[],[[[[]]]],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 3

[[[[]],[],[[]]]] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 4

[[[[]],[[]],[]]] => [[],[[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 4

[[[[]],[[],[]]]] => [[],[[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 4

[[[[]],[[[]]]]] => [[],[[],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 5

[[[[],[]],[],[]]] => [[[]],[[[]]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 3

[[[[[]]],[],[]]] => [[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4

[[[[],[]],[[]]]] => [[[]],[[],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[]]],[[]]]] => [[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5

[[[[],[],[]],[]]] => [[[[]]],[[]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 3

[[[[],[[]]],[]]] => [[[],[]],[[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[]],[]],[]]] => [[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[],[]]],[]]] => [[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[[]]]],[]]] => [[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5

[[[[],[],[],[]]]] => [[[[[]]]],[],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 3

[[[[],[],[[]]]]] => [[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 4

[[[[],[[]],[]]]] => [[[],[[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 4

[[[[],[[],[]]]]] => [[[[]],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 4

[[[[],[[[]]]]]] => [[[],[],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 5

[[[[[]],[],[]]]] => [[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4

[[[[[]],[[]]]]] => [[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5

[[[[[],[]],[]]]] => [[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4

[[[[[[]]],[]]]] => [[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5

[[[[[],[],[]]]]] => [[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4

[[[[[],[[]]]]]] => [[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5

[[[[[[]],[]]]]] => [[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5

[[[[[[],[]]]]]] => [[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5

[[[[[[[]]]]]]] => [[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6

[[],[],[],[],[],[],[]] => [[[[[[[[]]]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[[],[],[],[],[],[[]]] => [[[[[[[],[]]]]]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8) => 2

[[],[],[],[],[[]],[]] => [[[[[[],[[]]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2

[[],[],[],[],[[],[]]] => [[[[[[[]],[]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8) => 2

[[],[],[],[],[[[]]]] => [[[[[[],[],[]]]]]] => ([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8) => 3

[[],[],[],[[[]]],[]] => [[[[[],[],[[]]]]]] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8) => 3

[[],[],[],[[[]],[]]] => [[[[[],[[]],[]]]]] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8) => 3

[[],[],[],[[[],[]]]] => [[[[[[]],[],[]]]]] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8) => 3

[[],[],[],[[[[]]]]] => [[[[[],[],[],[]]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8) => 4

[[[[[]]]],[[[]]]] => [[],[],[],[[],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 6

[[[[[[]]]]],[[]]] => [[],[],[],[],[[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 6

[[[[[[[]]]]]],[]] => [[],[],[],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 6

[[[[[]]],[[[]]]]] => [[],[],[[],[],[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 6

[[[[[[]]]],[[]]]] => [[],[],[],[[],[]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 6

[[[[[[[]]]]],[]]] => [[],[],[],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 6

[[[[[]],[[[]]]]]] => [[],[[],[],[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 6

[[[[[[]]],[[]]]]] => [[],[],[[],[]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 6

[[[[[[[]]]],[]]]] => [[],[],[],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 6

[[[[[],[[[]]]]]]] => [[[],[],[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 6

[[[[[[]],[[]]]]]] => [[],[[],[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 6

[[[[[[[]]],[]]]]] => [[],[],[[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 6

[[[[[[],[[]]]]]]] => [[[],[]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 6

[[[[[[[]],[]]]]]] => [[],[[]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 6

[[[[[[[],[]]]]]]] => [[[]],[],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 6

[[[[[[[[]]]]]]]] => [[],[],[],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 7

[[],[],[],[],[],[],[],[]] => [[[[[[[[[]]]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[[[]],[[]],[[]],[[]]] => [[],[[],[[],[[],[]]]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 5

[[[]],[[]],[[],[[]]]] => [[],[[],[[[],[]],[]]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 5

[[[]],[[],[[]]],[[]]] => [[],[[[],[]],[[],[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9) => 5

[[[]],[[],[[]],[[]]]] => [[],[[[],[[],[]]],[]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 5

[[[]],[[],[[],[[]]]]] => [[],[[[[],[]],[]],[]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 5

[[[],[[]]],[[]],[[]]] => [[[],[]],[[],[[],[]]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => 5

[[[],[[]]],[[],[[]]]] => [[[],[]],[[[],[]],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => 5

[[[],[[]],[[]]],[[]]] => [[[],[[],[]]],[[],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => 5

[[[],[[],[[]]]],[[]]] => [[[[],[]],[]],[[],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => 5

[[[],[[]],[[]],[[]]]] => [[[],[[],[[],[]]]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 5

[[[],[[]],[[],[[]]]]] => [[[],[[[],[]],[]]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 5

[[[],[[],[[]]],[[]]]] => [[[[],[]],[[],[]]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9) => 5

[[[],[[],[[]],[[]]]]] => [[[[],[[],[]]],[]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 5

[[[],[[],[[],[[]]]]]] => [[[[[],[]],[]],[]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => 5

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Description

The number of minimal elements in a poset.

Map

to poset

Description

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

Map

DeBruijn-Morselt plane tree automorphism

Description

This automorphism on the set of plane trees with a given number of vertices is the combination of the two "canonical" bijections between plane trees and binary trees, using either the left or right branches. In [3] Shapiro essentially attributes this automorphism to DeBruijn and Morselt [1], hence the name I chose. Shapiro shows in that paper that for a large subset of plane trees (those corresponding to compositions), the sixth power of the automorphism acts as the identity on this subset. However, its behavior in general is quite chaotic. In [2] Donaghey studies this automorphism further and shows that its behavior on all trees can be reduced to its behavior on certain "primitive" trees.