Identifier
Values
[.,.] => [1,0] => [2,1] => ([(0,1)],2) => 2
[.,[.,.]] => [1,0,1,0] => [3,1,2] => ([(0,2),(1,2)],3) => 2
[[.,.],.] => [1,1,0,0] => [2,3,1] => ([(0,2),(1,2)],3) => 2
[.,[.,[.,.]]] => [1,0,1,0,1,0] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => 2
[.,[[.,.],.]] => [1,0,1,1,0,0] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => 2
[[.,.],[.,.]] => [1,1,1,0,0,0] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 2
[[.,[.,.]],.] => [1,1,0,0,1,0] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => 2
[.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[.,[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[[.,.],[.,[.,.]]] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[[[.,.],.],[.,.]] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[[.,[.,[.,.]]],.] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[[.,[[.,.],.]],.] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[[.,.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[[.,.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[.,.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[[[.,.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[[.,[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[[.,[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[.,[[.,.],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[.,[[.,[.,.]],.]],.] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 2
[.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 2
[.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 2
[.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 2
[.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 2
[.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 2
[.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2
[[.,.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[[.,.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[.,.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 2
[[.,.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 2
[[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[[[.,.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[.,.],[.,.]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => ([(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] => [2,7,1,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 2
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 2
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 2
[[.,[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 2
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 2
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 2
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 2
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[.,[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 2
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 2
>>> Load all 127 entries. <<<
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 2
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 2
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 2
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
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
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Map
pruning number to logarithmic height
Description
Francon's map from binary trees to Dyck paths.
This bijection sends the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree., to the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path.. The implementation is a literal translation of Knuth's [2].
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.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.