Identifier
Values
[1,0] => [.,.] => [[]] => ([(0,1)],2) => 0
[1,0,1,0] => [[.,.],.] => [[[]]] => ([(0,2),(1,2)],3) => 1
[1,1,0,0] => [.,[.,.]] => [[],[]] => ([(0,2),(1,2)],3) => 1
[1,0,1,0,1,0] => [[[.,.],.],.] => [[[[]]]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,1,0,0] => [[.,.],[.,.]] => [[[]],[]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,0,1,0] => [[.,[.,.]],.] => [[[],[]]] => ([(0,3),(1,3),(2,3)],4) => 1
[1,1,0,1,0,0] => [.,[[.,.],.]] => [[],[[]]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,0,0] => [.,[.,[.,.]]] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 1
[1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => [[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => [[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => [[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => [[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => [[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => [[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => [[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => [[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => [[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[1,1,0,1,1,0,0,0] => [.,[[.,.],[.,.]]] => [[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => [[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => [[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => [[[[[[]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => [[[[[]]]],[]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => [[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => [[[[]]],[[]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => [[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => [[[[[]],[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => [[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => [[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => [[[]],[[[]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => [[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => [[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => [[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => [[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => [[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => [[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => [[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => [[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => [[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => [[[[],[[]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => [[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => [[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[1,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],.],[.,.]]] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => [[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,.],.]]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[.,[.,.]]]] => [[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => [[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => [[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => [[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => [[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[.,.]],.]]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => [[[[[[[]]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => [[[[[[]]]]],[]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => [[[[[[]]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [[[[[]]]],[[]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[]]]],[],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => [[[[[[]]],[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[]]],[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => [[[[[]]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => [[[[]]],[[[]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => [[[[]]],[[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[]]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [[[[]]],[[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [[[[]]],[],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => [[[[[[]],[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[]],[]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[]],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [[[[]],[]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[]],[]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => [[[[[]],[[]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => [[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => [[[[]],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => [[[]],[[[[]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => [[[]],[[[]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => [[[[]],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [[[]],[[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => [[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => [[[[[]],[],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[]],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => [[[[]],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [[[]],[[[],[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => [[[]],[[],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => [[[[]],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [[[]],[[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [[[]],[],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => [[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => [[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [[[]],[],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => [[[[[[],[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[],[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => [[[[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[]]],[[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => [[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[]],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[]],[[[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[]],[[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[]],[],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => [[[[[],[[]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[]]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => [[[[],[[]]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[]]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => [[[[],[[[]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[]]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => [[[],[[[[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => [[],[[[[[]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => [[],[[[[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[[[]]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [[],[[[[]]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => [[[[],[[]],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => [[[],[[[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [[],[[[[]],[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[]],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [[],[[]],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => [[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => [[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => [[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => [[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[],[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => [[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [[],[[[[],[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => [[[],[[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [[],[[[],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => [[[[],[],[[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => [[[],[[],[[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [[],[[[],[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => [[],[[],[[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => [[[],[],[[[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [[],[[],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [[],[],[[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => [[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => [[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => [[],[],[[[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => [[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => [[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => [[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => [[],[[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => [[[],[],[[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => [[],[[],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,.]],[.,.]]]] => [[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => [[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => [[],[],[[],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [[],[],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of cut vertices of a graph.
A cut vertex is one whose deletion increases the number of connected components.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
  • if $x$ is the left child of $y$, $x$ becomes the first child of $y$.