Identifier
Values
[1,0] => [1] => [.,.] => [1,0] => 0
[1,0,1,0] => [2,1] => [[.,.],.] => [1,0,1,0] => 0
[1,1,0,0] => [1,2] => [.,[.,.]] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [3,2,1] => [[[.,.],.],.] => [1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => [2,3,1] => [[.,.],[.,.]] => [1,0,1,1,0,0] => 0
[1,1,0,0,1,0] => [3,1,2] => [[.,[.,.]],.] => [1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => [2,1,3] => [[.,.],[.,.]] => [1,0,1,1,0,0] => 0
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
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Description
The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
  • a leaf is associated with an empty Dyck path,
  • a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.