- FindStat

Identifier

Mp00139: Ordered trees —Zeilberger's Strahler bijection⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000639: Posets ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

[[],[[[]]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => ([(1,2),(2,3)],4) => 7

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

[[[]],[[]]] => [[.,[[.,.],.]],.] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => 8

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

[[[[]]],[]] => [[[.,[.,.]],.],.] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 9

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

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

[[[[]],[]]] => [[[.,.],.],[.,.]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 7

[[[[],[]]]] => [[[.,.],[.,.]],.] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 8

[[[[[]]]]] => [[[[.,.],.],.],.] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 10

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

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

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

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

[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 8

[[],[[]],[],[]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 8

[[],[[]],[[]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 9

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

[[],[[[]]],[]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 10

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

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

[[],[[[]],[]]] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 8

[[],[[[],[]]]] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 9

[[],[[[[]]]]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 11

[[[]],[],[],[]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 9

[[[]],[],[[]]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 10

[[[]],[[]],[]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 11

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

[[[]],[[[]]]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 12

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

[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 12

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

[[[[]]],[[]]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 13

[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 8

[[[],[[]]],[]] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 9

[[[[]],[]],[]] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 10

[[[[],[]]],[]] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 11

[[[[[]]]],[]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 14

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

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

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

[[[],[[],[]]]] => [[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 10

[[[],[[[]]]]] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 9

[[[[]],[],[]]] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 8

[[[[]],[[]]]] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 9

[[[[],[]],[]]] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 9

[[[[[]]],[]]] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 11

[[[[],[],[]]]] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 10

[[[[],[[]]]]] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 11

[[[[[]],[]]]] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 12

[[[[[],[]]]]] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 13

[[[[[[]]]]]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 15

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

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

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

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

[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 9

[[],[],[[]],[],[]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 9

[[],[],[[]],[[]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 10

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

[[],[],[[[]]],[]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => 11

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

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

[[],[],[[[]],[]]] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 9

[[],[],[[[],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 10

[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => 12

[[],[[]],[],[],[]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 10

[[],[[]],[],[[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11

[[],[[]],[[]],[]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 12

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

[[],[[]],[[[]]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 13

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

[[],[[[]]],[],[]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 13

[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 9

[[],[[[]]],[[]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 14

[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 9

[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 10

[[],[[[]],[]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 11

[[],[[[],[]]],[]] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 12

[[],[[[[]]]],[]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 15

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

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

[[],[[],[[]],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 9

[[],[[],[[],[]]]] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11

[[],[[],[[[]]]]] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => 10

[[],[[[]],[],[]]] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 9

[[],[[[]],[[]]]] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => 10

[[],[[[],[]],[]]] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => 10

[[],[[[[]]],[]]] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 12

[[],[[[],[],[]]]] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11

>>> Load all 473 entries. <<<

[[],[[[],[[]]]]] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 12

[[],[[[[]],[]]]] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 13

[[],[[[[],[]]]]] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 14

[[],[[[[[]]]]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 16

[[[]],[],[],[],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 11

[[[]],[],[],[[]]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 12

[[[]],[],[[]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 13

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

[[[]],[],[[[]]]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 14

[[[]],[[]],[],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 14

[[[]],[[]],[[]]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 15

[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 9

[[[]],[[[]]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 16

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

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

[[[]],[[[]],[]]] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 10

[[[]],[[[],[]]]] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 11

[[[]],[[[[]]]]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 17

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

[[[[]]],[],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 15

[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 9

[[[[]]],[],[[]]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 16

[[[],[]],[[]],[]] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 10

[[[[]]],[[]],[]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 17

[[[],[]],[[],[]]] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 9

[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 11

[[[[]]],[[],[]]] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 10

[[[[]]],[[[]]]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 18

[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 9

[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => 10

[[[[]],[]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => 11

[[[[],[]]],[],[]] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 13

[[[[[]]]],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 18

[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 10

[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 11

[[[[]],[]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => ([(0,5),(1,5),(2,3),(5,4)],6) => 12

[[[[],[]]],[[]]] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 14

[[[[[]]]],[[]]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 19

[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 10

[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11

[[[],[[]],[]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 12

[[[],[[],[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 13

[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 13

[[[[]],[],[]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 13

[[[[]],[[]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 14

[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 12

[[[[[]]],[]],[]] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 15

[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 14

[[[[],[[]]]],[]] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 15

[[[[[]],[]]],[]] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 16

[[[[[],[]]]],[]] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 17

[[[[[[]]]]],[]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 20

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

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

[[[],[],[[]],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 9

[[[],[],[[],[]]]] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 12

[[[],[],[[[]]]]] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => 10

[[[],[[]],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 10

[[[],[[]],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 11

[[[],[[],[]],[]]] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11

[[[],[[[]]],[]]] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 12

[[[],[[],[],[]]]] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 12

[[[],[[],[[]]]]] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 13

[[[],[[[]],[]]]] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 14

[[[],[[[],[]]]]] => [[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 15

[[[],[[[[]]]]]] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 13

[[[[]],[],[],[]]] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 9

[[[[]],[],[[]]]] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 10

[[[[]],[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 11

[[[[]],[[],[]]]] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 13

[[[[]],[[[]]]]] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 12

[[[[],[]],[],[]]] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => 10

[[[[[]]],[],[]]] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 12

[[[[],[]],[[]]]] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 11

[[[[[]]],[[]]]] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 13

[[[[],[],[]],[]]] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11

[[[[],[[]]],[]]] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 12

[[[[[]],[]],[]]] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 13

[[[[[],[]]],[]]] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 14

[[[[[[]]]],[]]] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 16

[[[[],[],[],[]]]] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 12

[[[[],[],[[]]]]] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 13

[[[[],[[]],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 14

[[[[],[[],[]]]]] => [[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 16

[[[[],[[[]]]]]] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 15

[[[[[]],[],[]]]] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 14

[[[[[]],[[]]]]] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 15

[[[[[],[]],[]]]] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 15

[[[[[[]]],[]]]] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 17

[[[[[],[],[]]]]] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 16

[[[[[],[[]]]]]] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 17

[[[[[[]],[]]]]] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 18

[[[[[[],[]]]]]] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 19

[[[[[[[]]]]]]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 21

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

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

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

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

[[],[],[],[],[[[]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => ([(4,5),(5,6)],7) => 10

[[],[],[],[[]],[],[]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => ([(3,6),(4,6),(5,6)],7) => 10

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

[[],[],[],[[[]]],[]] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => ([(3,6),(4,6),(6,5)],7) => 12

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

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

[[],[],[],[[[]],[]]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => ([(4,5),(5,6)],7) => 10

[[],[],[],[[[[]]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => ([(3,4),(4,6),(6,5)],7) => 13

[[],[],[[]],[],[],[]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11

[[],[],[[]],[],[[]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[],[],[[]],[[]],[]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13

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

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

[[],[],[[[]]],[],[]] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => 14

[[],[],[[],[]],[[]]] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => ([(2,6),(3,6),(4,5)],7) => 10

[[],[],[[],[],[]],[]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 10

[[],[],[[[]],[]],[]] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => ([(3,6),(4,6),(6,5)],7) => 12

[[],[],[[[],[]]],[]] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13

[[],[],[[[[]]]],[]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 16

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

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

[[],[],[[],[[]],[]]] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => ([(2,6),(3,6),(4,5)],7) => 10

[[],[],[[],[[],[]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[],[],[[[]],[],[]]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => 10

[[],[],[[[[]]],[]]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => ([(3,4),(4,6),(6,5)],7) => 13

[[],[],[[[],[],[]]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[],[[]],[],[],[],[]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 12

[[],[[]],[],[],[[]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13

[[],[[]],[],[[]],[]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14

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

[[],[[]],[],[[[]]]] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15

[[],[[]],[[]],[],[]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 15

[[],[[]],[[],[]],[]] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => ([(2,6),(3,6),(4,5)],7) => 10

[[],[[]],[[[]]],[]] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 17

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

[[],[[]],[[[[]]]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 18

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

[[],[[[]]],[],[],[]] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 16

[[],[[],[]],[],[[]]] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => 10

[[],[[[]]],[],[[]]] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17

[[],[[],[]],[[]],[]] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11

[[],[[[]]],[[]],[]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18

[[],[[],[]],[[],[]]] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => 10

[[],[[],[]],[[[]]]] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12

[[],[[],[],[]],[],[]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => ([(3,6),(4,6),(5,6)],7) => 10

[[],[[[]],[]],[],[]] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => ([(3,6),(4,6),(6,5)],7) => 12

[[],[[[],[]]],[],[]] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14

[[],[[[[]]]],[],[]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 19

[[],[[],[],[]],[[]]] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11

[[],[[[]],[]],[[]]] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13

[[],[[[],[]]],[[]]] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[],[[],[],[],[]],[]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11

[[],[[],[],[[]]],[]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[],[[],[[]],[]],[]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13

[[],[[],[[],[]]],[]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14

[[],[[[]],[],[]],[]] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => 14

[[],[[[],[]],[]],[]] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13

[[],[[[[]]],[]],[]] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 16

[[],[[[],[],[]]],[]] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 15

[[],[[[[]],[]]],[]] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 17

[[],[[[[],[]]]],[]] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18

[[],[[[[[]]]]],[]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 21

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

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

[[],[[],[],[[]],[]]] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => ([(2,6),(3,6),(4,5)],7) => 10

[[],[[],[],[[],[]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13

[[],[[],[[]],[],[]]] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11

[[],[[],[[],[]],[]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[],[[],[[[]]],[]]] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13

[[],[[],[[],[],[]]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13

[[],[[],[[[]],[]]]] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15

[[],[[[]],[],[],[]]] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 10

[[],[[[]],[[]],[]]] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12

[[],[[[[]]],[],[]]] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => ([(3,4),(4,6),(6,5)],7) => 13

[[],[[[],[],[]],[]]] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[],[[[],[],[],[]]]] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13

[[],[[[],[[]],[]]]] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[],[[[],[[],[]]]]] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17

[[],[[[[]],[],[]]]] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15

[[],[[[[[]]],[]]]] => [.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 18

[[],[[[[],[],[]]]]] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17

[[[]],[],[],[],[],[]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 13

[[[]],[],[],[],[[]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14

[[[]],[],[],[[]],[]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 15

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

[[[]],[],[],[[[]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 16

[[[]],[],[[]],[],[]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 16

[[[]],[],[[]],[[]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17

[[[]],[],[[],[]],[]] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 10

[[[]],[],[[[]]],[]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 18

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

[[[]],[],[[[[]]]]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 19

[[[]],[[]],[],[],[]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 17

[[[]],[[]],[],[[]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18

[[[]],[[]],[[]],[]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 19

[[[]],[[],[]],[],[]] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => ([(2,6),(3,6),(4,5)],7) => 10

[[[]],[[[]]],[],[]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 20

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

[[[]],[[[]]],[[]]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 21

[[[]],[[],[],[]],[]] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11

[[[]],[[[]],[]],[]] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13

[[[]],[[[],[]]],[]] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 14

[[[]],[[[[]]]],[]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 22

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

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

[[[]],[[],[[],[]]]] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13

[[[]],[[[],[],[]]]] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13

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

[[[[]]],[],[],[],[]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 18

[[[],[]],[],[],[[]]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10

[[[[]]],[],[],[[]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 19

[[[],[]],[],[[]],[]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11

[[[[]]],[],[[]],[]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 20

[[[],[]],[],[[],[]]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10

[[[],[]],[],[[[]]]] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12

[[[[]]],[],[[[]]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 21

[[[],[]],[[]],[],[]] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 12

[[[[]]],[[]],[],[]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 21

[[[],[]],[[]],[[]]] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 13

[[[],[]],[[],[]],[]] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11

[[[],[]],[[[]]],[]] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 14

[[[[]]],[[],[]],[]] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12

[[[[]]],[[[]]],[]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 23

[[[],[]],[[],[],[]]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10

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

[[[],[]],[[[]],[]]] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12

[[[],[]],[[[],[]]]] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 13

[[[],[]],[[[[]]]]] => [[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 15

[[[[]]],[[[[]]]]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 24

[[[],[],[]],[],[],[]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => 10

[[[[]],[]],[],[],[]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => ([(3,6),(4,6),(6,5)],7) => 12

[[[[],[]]],[],[],[]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 15

[[[[[]]]],[],[],[]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 22

[[[],[],[]],[],[[]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11

[[[[]],[]],[],[[]]] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13

[[[[],[]]],[],[[]]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16

[[[[[]]]],[],[[]]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 23

[[[],[],[]],[[]],[]] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 12

[[[],[[]]],[[]],[]] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 13

[[[[]],[]],[[]],[]] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 14

[[[[],[]]],[[]],[]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 17

[[[[[]]]],[[]],[]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 24

[[[],[],[]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11

[[[],[],[]],[[[]]]] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 13

[[[[]],[]],[[],[]]] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13

[[[[]],[]],[[[]]]] => [[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 15

[[[[],[]]],[[],[]]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16

[[[[],[]]],[[[]]]] => [[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 18

[[[],[],[],[]],[],[]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11

[[[],[],[[]]],[],[]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[[],[[]],[]],[],[]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13

[[[],[[],[]]],[],[]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 15

[[[[]],[],[]],[],[]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => ([(2,6),(3,6),(4,6),(6,5)],7) => 14

[[[[],[]],[]],[],[]] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14

[[[[[]]],[]],[],[]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => ([(2,6),(3,6),(4,5),(6,4)],7) => 16

[[[[],[],[]]],[],[]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 16

[[[[],[[]]]],[],[]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17

[[[[[]],[]]],[],[]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 18

[[[[[],[]]]],[],[]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 20

[[[[[[]]]]],[],[]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 25

[[[],[],[],[]],[[]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 12

[[[],[],[[]]],[[]]] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13

[[[],[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 14

[[[],[[],[]]],[[]]] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16

[[[[]],[],[]],[[]]] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 15

[[[[],[]],[]],[[]]] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[[[[]]],[]],[[]]] => [[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 17

[[[[],[],[]]],[[]]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 17

[[[[[]],[]]],[[]]] => [[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 19

[[[[[],[]]]],[[]]] => [[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 21

[[[],[],[],[],[]],[]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 12

[[[],[],[],[[]]],[]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13

[[[],[],[[]],[]],[]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14

[[[],[],[[],[]]],[]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 15

[[[],[],[[[]]]],[]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15

[[[],[[]],[],[]],[]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 15

[[[],[[],[]],[]],[]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14

[[[],[[[]]],[]],[]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 17

[[[],[[],[],[]]],[]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 16

[[[],[[],[[]]]],[]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17

[[[],[[[]],[]]],[]] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 18

[[[],[[[],[]]]],[]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 19

[[[],[[[[]]]]],[]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 18

[[[[]],[],[],[]],[]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 16

[[[[]],[],[[]]],[]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17

[[[[]],[[]],[]],[]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18

[[[[]],[[],[]]],[]] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16

[[[[],[]],[],[]],[]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13

[[[[[]]],[],[]],[]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 19

[[[[],[]],[[]]],[]] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 14

[[[[],[],[]],[]],[]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 15

[[[[[]],[]],[]],[]] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 17

[[[[[],[]]],[]],[]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18

[[[[[[]]]],[]],[]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 21

[[[[],[],[],[]]],[]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 17

[[[[],[],[[]]]],[]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18

[[[[],[[]],[]]],[]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 19

[[[[],[[],[]]]],[]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 20

[[[[[]],[],[]]],[]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 20

[[[[[]],[[]]]],[]] => [[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 21

[[[[[],[]],[]]],[]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 19

[[[[[[]]],[]]],[]] => [[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 22

[[[[[],[],[]]]],[]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 21

[[[[[[]],[]]]],[]] => [[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 23

[[[[[[],[]]]]],[]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 24

[[[[[[[]]]]]],[]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 27

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

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

[[[],[],[],[[]],[]]] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 10

[[[],[],[],[[],[]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14

[[[],[],[[]],[],[]]] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11

[[[],[],[[],[]],[]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13

[[[],[],[[[]]],[]]] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13

[[[],[],[[],[],[]]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14

[[[],[],[[],[[]]]]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[[],[],[[[]],[]]]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 16

[[[],[],[[[],[]]]]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17

[[[],[[]],[],[],[]]] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 12

[[[],[[]],[],[[]]]] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13

[[[],[[]],[[]],[]]] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 14

[[[],[[]],[[],[]]]] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[[],[[],[]],[],[]]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[[],[[[]]],[],[]]] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 15

[[[],[[],[]],[[]]]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13

[[[],[[],[],[]],[]]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13

[[[],[[[]],[]],[]]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15

[[[],[[[[]]]],[]]] => [[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 17

[[[],[[],[],[],[]]]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14

[[[],[[],[],[[]]]]] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[[],[[],[[]],[]]]] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16

[[[],[[],[[],[]]]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18

[[[],[[[]],[],[]]]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 16

[[[],[[[],[]],[]]]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17

[[[],[[[[]]],[]]]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 19

[[[],[[[],[],[]]]]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18

[[[],[[[[],[]]]]]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 21

[[[[]],[],[],[],[]]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => 10

[[[[]],[],[[]],[]]] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12

[[[[]],[],[[],[]]]] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[[[]],[[]],[],[]]] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 13

[[[[]],[[[]]],[]]] => [[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 15

[[[[]],[[],[],[]]]] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[[[[]]],[],[],[]]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 13

[[[[],[]],[[]],[]]] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 13

[[[[[]]],[[]],[]]] => [[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 15

[[[[],[],[]],[],[]]] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12

[[[[],[],[]],[[]]]] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13

[[[[],[],[],[]],[]]] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13

[[[[],[[]],[]],[]]] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[[[],[[],[]]],[]]] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17

[[[[[]],[],[]],[]]] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15

[[[[[[]]],[]],[]]] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 18

[[[[[],[],[]]],[]]] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17

[[[[],[],[],[],[]]]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14

[[[[],[],[],[[]]]]] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15

[[[[],[],[[]],[]]]] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16

[[[[],[],[[],[]]]]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 19

[[[[],[[]],[],[]]]] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 17

[[[[],[[],[]],[]]]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18

[[[[],[[[]]],[]]]] => [[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 19

[[[[],[[],[],[]]]]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 19

[[[[],[[[]],[]]]]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 21

[[[[[]],[],[],[]]]] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 16

[[[[[]],[[]],[]]]] => [[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 18

[[[[[],[]],[],[]]]] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17

[[[[[[]]],[],[]]]] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 19

[[[[[],[],[]],[]]]] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18

[[[[[[],[]]],[]]]] => [[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 21

[[[[[],[],[],[]]]]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 19

[[[[[],[[]],[]]]]] => [[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 21

[[[[[],[[],[]]]]]] => [[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 23

[[[[[[]],[],[]]]]] => [[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 21

[[[[[[[]]],[]]]]] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 24

[[[[[[],[],[]]]]]] => [[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 23

search for individual values

searching the database for the individual values of this statistic

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searching the database for statistics with the same generating function

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

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

$F_{5} = q^{4} + 3\ q^{5} + 3\ q^{6} + 3\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$

$F_{6} = q^{5} + 4\ q^{6} + 6\ q^{7} + 7\ q^{8} + 7\ q^{9} + 5\ q^{10} + 5\ q^{11} + 3\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$

$F_{7} = q^{6} + 5\ q^{7} + 10\ q^{8} + 14\ q^{9} + 17\ q^{10} + 16\ q^{11} + 16\ q^{12} + 14\ q^{13} + 11\ q^{14} + 9\ q^{15} + 7\ q^{16} + 5\ q^{17} + 3\ q^{18} + 2\ q^{19} + q^{20} + q^{21}$

Description

The number of relations in a poset.
This is the number of intervals

$x,y$ with

$x\leq y$ in the poset, and therefore the dimension of the posets incidence algebra.

Map

Zeilberger's Strahler bijection

Description

Zeilberger's Strahler bijection between ordered and binary trees.
This is a bijection sending the pruning number of the ordered tree to the Strahler number of the binary tree.

Map

to 132-avoiding permutation

Description

Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation

$\pi$ of length

$n$ , this poset has vertices

$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$
and the cover relation is given by

$(w, x) \leq (y, z)$ if

$w \leq y$ and

$x \leq z$ .
For example, the permutation

$[3,1,5,4,2]$ is mapped to the poset with cover relations

$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$