Identifier
Values
[[]] => [.,.] => [1] => ([],1) => 0
[[],[]] => [[.,.],.] => [1,2] => ([],2) => 0
[[[]]] => [.,[.,.]] => [2,1] => ([(0,1)],2) => 1
[[],[],[]] => [[[.,.],.],.] => [1,2,3] => ([],3) => 0
[[],[[]]] => [[.,.],[.,.]] => [1,3,2] => ([(1,2)],3) => 0
[[[]],[]] => [[.,[.,.]],.] => [2,1,3] => ([(1,2)],3) => 0
[[[],[]]] => [.,[[.,.],.]] => [2,3,1] => ([(0,2),(1,2)],3) => 1
[[[[]]]] => [.,[.,[.,.]]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => 2
[[],[],[],[]] => [[[[.,.],.],.],.] => [1,2,3,4] => ([],4) => 0
[[],[],[[]]] => [[[.,.],.],[.,.]] => [1,2,4,3] => ([(2,3)],4) => 0
[[],[[]],[]] => [[[.,.],[.,.]],.] => [1,3,2,4] => ([(2,3)],4) => 0
[[],[[],[]]] => [[.,.],[[.,.],.]] => [1,3,4,2] => ([(1,3),(2,3)],4) => 0
[[],[[[]]]] => [[.,.],[.,[.,.]]] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => 0
[[[]],[],[]] => [[[.,[.,.]],.],.] => [2,1,3,4] => ([(2,3)],4) => 0
[[[]],[[]]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => ([(0,3),(1,2)],4) => 1
[[[],[]],[]] => [[.,[[.,.],.]],.] => [2,3,1,4] => ([(1,3),(2,3)],4) => 0
[[[[]]],[]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => 0
[[[],[],[]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 1
[[[],[[]]]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 1
[[[[]],[]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 1
[[[[],[]]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[[[[]]]]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[],[],[],[],[]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => ([],5) => 0
[[],[],[],[[]]] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => ([(3,4)],5) => 0
[[],[],[[]],[]] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => ([(3,4)],5) => 0
[[],[],[[],[]]] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => 0
[[],[],[[[]]]] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5) => 0
[[],[[]],[],[]] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => ([(3,4)],5) => 0
[[],[[]],[[]]] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => 0
[[],[[],[]],[]] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => 0
[[],[[[]]],[]] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5) => 0
[[],[[],[],[]]] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 0
[[],[[],[[]]]] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 0
[[],[[[]],[]]] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 0
[[],[[[],[]]]] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[],[[[[]]]]] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[]],[],[],[]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => ([(3,4)],5) => 0
[[[]],[],[[]]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => 0
[[[]],[[]],[]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => 0
[[[]],[[],[]]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => 1
[[[]],[[[]]]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5) => 1
[[[],[]],[],[]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => 0
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => 0
[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => 1
[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5) => 1
[[[],[],[]],[]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => 0
[[[],[[]]],[]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[[]],[]],[]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[[],[]]],[]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[[[]]]],[]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
[[[],[],[],[]]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[[[],[],[[]]]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[],[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[],[[],[]]]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[],[[[]]]]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[[]],[],[]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[[]],[[]]]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 2
[[[[],[]],[]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[[[]]],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[[[],[],[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[[[],[[]]]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[[[[]],[]]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[[[[],[]]]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[[[[[]]]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[[],[],[],[],[],[]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => ([],6) => 0
[[],[],[],[],[[]]] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => ([(4,5)],6) => 0
[[],[],[],[[]],[]] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => ([(4,5)],6) => 0
[[],[],[],[[],[]]] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => 0
[[],[],[],[[[]]]] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6) => 0
[[],[],[[]],[],[]] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => ([(4,5)],6) => 0
[[],[],[[]],[[]]] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => 0
[[],[],[[],[]],[]] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => 0
[[],[],[[[]]],[]] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6) => 0
[[],[],[[],[],[]]] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => 0
[[],[],[[],[[]]]] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[],[[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[],[[[],[]]]] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[],[[[[]]]]] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[]],[],[],[]] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => ([(4,5)],6) => 0
[[],[[]],[],[[]]] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => 0
[[],[[]],[[]],[]] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => 0
[[],[[]],[[],[]]] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 0
[[],[[]],[[[]]]] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 0
[[],[[],[]],[],[]] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => 0
[[],[[[]]],[],[]] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => ([(3,4),(3,5),(4,5)],6) => 0
[[],[[],[]],[[]]] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => 0
[[],[[[]]],[[]]] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => 0
[[],[[],[],[]],[]] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => 0
[[],[[],[[]]],[]] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[]],[]],[]] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[],[]]],[]] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[[]]]],[]] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[],[],[],[]]] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[[],[[],[],[[]]]] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[],[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[],[[],[]]]] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[],[[[]]]]] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[]],[],[]]] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[]],[[]]]] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
[[],[[[],[]],[]]] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[[]]],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
>>> Load all 196 entries. <<<
[[],[[[],[],[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[],[[]]]]] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[[]],[]]]] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[[],[]]]]] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[],[[[[[]]]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[]],[],[],[],[]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => ([(4,5)],6) => 0
[[[]],[],[],[[]]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => 0
[[[]],[],[[]],[]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => 0
[[[]],[],[[],[]]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 0
[[[]],[],[[[]]]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => 0
[[[]],[[]],[],[]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => 0
[[[]],[[]],[[]]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => 1
[[[]],[[],[]],[]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => 0
[[[]],[[[]]],[]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => ([(1,2),(3,4),(3,5),(4,5)],6) => 0
[[[]],[[],[],[]]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => 1
[[[]],[[],[[]]]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[]],[[[]],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[]],[[[],[]]]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[]],[[[[]]]]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[]],[],[],[]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => 0
[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => 0
[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 0
[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => 0
[[[],[]],[[]],[]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 0
[[[[]]],[[]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => ([(1,2),(3,4),(3,5),(4,5)],6) => 0
[[[],[]],[[],[]]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[[[],[]],[[[]]]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 1
[[[[]]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 1
[[[[]]],[[[]]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 2
[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => 0
[[[],[[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 1
[[[],[[]]],[[]]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[],[],[]],[]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
[[[],[],[[]]],[]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[],[[]],[]],[]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[],[[],[]]],[]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[],[[[]]]],[]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[]],[],[]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[]],[[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
[[[[],[]],[]],[]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[[]]],[]],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[],[],[]]],[]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[],[[]]]],[]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[[]],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[[],[]]]],[]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[[[[]]]]],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
[[[],[],[],[],[]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[[[],[],[],[[]]]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[],[[]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[],[[],[]]]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[],[[[]]]]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[[]],[],[]]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[[]],[[]]]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 1
[[[],[[],[]],[]]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[[[]]],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[[],[],[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[[],[[]]]]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[[[]],[]]]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[[[],[]]]]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[],[[[[]]]]]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[]],[],[],[]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[]],[],[[]]]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 1
[[[[]],[[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 1
[[[[]],[[],[]]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[]],[[[]]]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[]],[],[]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[],[]],[[]]]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[[]]],[[]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[],[]],[]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[],[[]]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[[]],[]],[]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[[],[]]],[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[[[]]]],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[[[[],[],[],[]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[],[[]]]]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[[]],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[[],[]]]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[],[[[]]]]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[[]],[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[[]],[[]]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[[[[],[]],[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[[[]]],[]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[[[[],[],[]]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[[[[],[[]]]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[[[[[]],[]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[[[[[],[]]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[[[[[[[]]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
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Description
The minimal degree of a vertex of a graph.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
to 312-avoiding permutation
Description
Return a 312-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 minimal element of this Sylvester class.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.