Identifier
Values
[1] => [1,0,1,0] => [.,[.,.]] => [2,1] => 0
[2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => [2,1,3] => 0
[1,1] => [1,0,1,1,0,0] => [.,[[.,.],.]] => [2,3,1] => 1
[3] => [1,1,1,0,0,0,1,0] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 0
[2,1] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => [3,2,1] => 0
[1,1,1] => [1,0,1,1,1,0,0,0] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 0
[3,1] => [1,1,0,1,0,0,1,0] => [[[.,[.,.]],.],.] => [2,1,3,4] => 0
[2,2] => [1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],.] => [2,3,1,4] => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => [.,[[[.,.],.],.]] => [2,3,4,1] => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 2
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 0
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 0
[3,2] => [1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 0
[3,1,1] => [1,0,1,1,0,0,1,0] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 1
[2,2,1] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 2
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 2
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 0
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 1
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 0
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 0
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 3
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 1
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 2
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 3
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 0
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 1
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 0
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 1
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 3
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 2
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 3
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 1
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 0
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 0
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 2
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 0
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 1
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 2
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 4
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 3
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 4
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 1
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 3
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 0
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 1
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 1
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 0
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 0
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 3
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 3
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 3
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 1
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 4
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 0
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 2
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 1
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 0
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 1
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 3
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 2
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 4
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 0
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 5
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 3
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 4
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 1
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 2
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 3
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 1
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 0
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 2
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 0
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 3
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 1
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 3
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 1
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 4
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 3
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 4
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 5
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 2
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 3
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 4
>>> Load all 228 entries. <<<
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 0
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 0
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 1
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 1
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 2
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 3
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 2
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 2
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 3
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 4
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 4
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 5
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 6
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 3
[7,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 0
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 0
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 1
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 2
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 3
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 4
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 3
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 4
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 5
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 2
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 6
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 0
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 1
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 2
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 5
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 3
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 4
[7,5,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 1
[7,4,3,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 0
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 1
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 2
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 0
[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 2
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 3
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 3
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 2
[7,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 0
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 2
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 0
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 0
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 5
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 1
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 6
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 2
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 3
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 4
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 5
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 5
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 4
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 6
[7,5,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 2
[7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 0
[6,6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 4
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 1
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 2
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 0
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 1
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 3
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 4
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 2
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 4
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 5
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 6
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 7
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 4
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 3
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 0
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 4
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 3
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 0
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 4
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 3
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 6
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 2
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 5
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 1
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 0
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 0
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 0
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 0
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 5
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 4
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 1
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 6
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 0
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 5
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 4
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 8
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 4
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 3
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 5
[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 1
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 0
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 0
[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 0
[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 0
[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 0
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 0
[6,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 5
[6,5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 8
[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 0
[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 0
[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 0
[6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 6
[8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 0
[7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 7
[9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 0
[8,7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 8
[8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 0
[8,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 0
[8,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 0
[8,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 0
[8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 0
[9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 0
[8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => 0
[9,7,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 0
[7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 6
[8,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 7
[9,8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => 0
[10,9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 0
[8,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 5
[7,6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 6
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Description
The number of occurrences of the pattern 23-1.
See Permutations/#Pattern-avoiding_permutations for the definition of the pattern $23\!\!-\!\!1$.
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 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
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.