Identifier
Values
[1,0] => [1,1,0,0] => [[.,.],.] => [1,2] => 0
[1,0,1,0] => [1,1,0,1,0,0] => [[[.,.],.],.] => [1,2,3] => 0
[1,1,0,0] => [1,1,1,0,0,0] => [[.,.],[.,.]] => [3,1,2] => 0
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [[[[.,.],.],.],.] => [1,2,3,4] => 0
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],.] => [3,1,2,4] => 0
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[.,.],[[.,.],.]] => [3,4,1,2] => 0
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,.]] => [4,2,1,3] => 1
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [[[.,.],.],[.,.]] => [4,1,2,3] => 0
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 0
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 0
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 1
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 0
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 0
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 0
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 1
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 2
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 0
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 0
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 1
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 0
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 0
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 0
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 0
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 0
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 0
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 3
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 1
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 0
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 0
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 1
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 0
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => 0
>>> Load all 152 entries. <<<
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => 0
[] => [1,0] => [.,.] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => 0
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Description
The number of adjacencies of a permutation.
An adjacency of a permutation $\pi$ is an index $i$ such that $\pi(i)-1 = \pi(i+1)$. Adjacencies are also known as small descents.
This can be also described as an occurrence of the bivincular pattern ([2,1], {((0,1),(1,0),(1,1),(1,2),(2,1)}), i.e., the middle row and the middle column are shaded, see [3].
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
logarithmic height to pruning number
Description
Francon's map from Dyck paths to binary trees.
This bijection sends the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path., to the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree.. The implementation is a literal translation of Knuth's [2].
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.