- FindStat

Identifier

Mp00047: Ordered trees —to poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ Lattices
St000550: Lattices ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 301 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[],[[],[[],[[],[[],[]]]]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[],[[],[[],[[[],[]],[]]]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[],[[],[[[],[]],[[],[]]]]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 7

[[],[[],[[[],[[],[]]],[]]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[],[[],[[[[],[]],[]],[]]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[],[[[],[[],[[],[]]]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[],[[[],[[[],[]],[]]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[],[[[[],[]],[[],[]]],[]]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 7

[[],[[[[],[[],[]]],[]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[],[[[[[],[]],[]],[]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[[],[[],[[],[[],[]]]]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[[],[[],[[[],[]],[]]]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[[],[[[],[]],[[],[]]]],[]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 7

[[[],[[[],[[],[]]],[]]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[[],[[[[],[]],[]],[]]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[[[],[[],[[],[]]]],[]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[[[],[[[],[]],[]]],[]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[[[[],[]],[[],[]]],[]],[]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 7

[[[[[],[[],[]]],[]],[]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[[[[[],[]],[]],[]],[]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[[],[[],[[],[[],[[],[[],[]]]]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[],[[],[[],[[[],[]],[]]]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[],[[],[[[],[[],[]]],[]]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[],[[],[[[[],[]],[]],[]]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[],[[[],[[],[[],[]]]],[]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[],[[[],[[[],[]],[]]],[]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[],[[[[],[[],[]]],[]],[]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[],[[[[[],[]],[]],[]],[]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[[],[[],[[],[[],[]]]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[[],[[],[[[],[]],[]]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[[],[[[],[[],[]]],[]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[[],[[[[],[]],[]],[]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[[[],[[],[[],[]]]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[[[],[[[],[]],[]]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[[[[],[[],[]]],[]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[],[[[[[[],[]],[]],[]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[],[[],[[],[[],[[],[]]]]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[],[[],[[],[[[],[]],[]]]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[],[[],[[[],[[],[]]],[]]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[],[[],[[[[],[]],[]],[]]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[],[[[],[[],[[],[]]]],[]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[],[[[],[[[],[]],[]]],[]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[],[[[[],[[],[]]],[]],[]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[],[[[[[],[]],[]],[]],[]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[[],[[],[[],[[],[]]]]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[[],[[],[[[],[]],[]]]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[[],[[[],[[],[]]],[]]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[[],[[[[],[]],[]],[]]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[[[],[[],[[],[]]]],[]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[[[],[[[],[]],[]]],[]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[[[[],[[],[]]],[]],[]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[[[[[[[],[]],[]],[]],[]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

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$F_{1} = q$

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

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

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

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

$F_{6} = q^{2} + 10\ q^{3} + 15\ q^{4} + 12\ q^{5} + 2\ q^{6} + 2\ q^{7}$

Description

The number of modular elements of a lattice.
A pair

$(x, y)$ of elements of a lattice

$L$ is a modular pair if for every

$z\geq y$ we have that

$(y\vee x) \wedge z = y \vee (x \wedge z)$ . An element

$x$ is left-modular if

$(x, y)$ is a modular pair for every

$y\in L$ , and is modular if both

$(x, y)$ and

$(y, x)$ are modular pairs for every

$y\in L$ .

Map

maximal antichains

Description

The lattice of maximal antichains in a poset.
An antichain

$A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of

$A$ .
The set of maximal antichains can be ordered by setting

$A \leq B \Leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow}B$ , where

$\mathop{\downarrow}A$ is the order ideal generated by

$A$ .

Map

to poset

Description

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