Identifier
Values
[1] => [1,0] => [1,0] => [.,.] => 0
[1,1] => [1,0,1,0] => [1,1,0,0] => [[.,.],.] => 0
[2] => [1,1,0,0] => [1,0,1,0] => [.,[.,.]] => 0
[1,1,1] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [[.,.],[.,.]] => 0
[1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 0
[2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => [.,[[.,.],.]] => 0
[3] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => [[[.,.],.],.] => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[[.,.],.],[.,.]] => 0
[1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [[.,.],[.,[.,.]]] => 0
[1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],.] => 0
[1,3] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [[.,.],[[.,.],.]] => 0
[2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => [.,[[.,.],[.,.]]] => 0
[2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => [.,[[.,[.,.]],.]] => 0
[3,1] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],.] => 0
[4] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,.]] => 0
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,.]] => 0
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[.,[.,.]]] => 0
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => 0
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 0
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],.] => 0
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 0
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 0
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [[[.,[.,.]],.],[.,.]] => 0
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,.]]] => 0
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[.,[.,.]]]] => 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],.]] => 0
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[[.,.],.]]] => 0
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [[[[.,.],.],[.,.]],.] => 0
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 0
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,.]] => 0
[5] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[.,.]] => 0
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 0
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => 0
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 0
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => 0
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],.]]] => 0
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => 0
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => 0
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],.],[.,.]]],.] => 0
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 1
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],.] => 0
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],.] => 0
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => 0
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],[.,.]] => 0
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[.,.],.],[.,.]],[.,.]] => 0
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 1
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 0
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => 0
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],.]] => 0
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => 1
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => 0
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[[.,.],[.,.]],[.,.]],.] => 0
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => 0
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],.] => 0
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[[.,.],.]],.] => 0
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => 0
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => 0
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 0
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => 0
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 0
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 0
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 0
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => 0
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 1
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 0
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 0
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 0
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 1
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 0
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 1
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => 0
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 1
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => 0
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => 0
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 0
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 1
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => 1
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => 0
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 0
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 0
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => 1
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => 0
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 0
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 1
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 1
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => 0
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => 0
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 0
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 0
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 0
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 0
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => 0
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => 1
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 0
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 1
>>> Load all 127 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 1
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 0
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => 0
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 1
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 0
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => 0
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 1
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => 0
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 0
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => 0
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 0
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => 0
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => 0
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 1
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => 0
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => 0
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => 0
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => 0
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 1
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 0
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => 0
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => 0
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 0
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 0
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => 0
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Description
The number of occurrences of the contiguous pattern [.,[.,[.,[.,.]]]] in a binary tree.
oeis:A036765 counts binary trees avoiding this pattern.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
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].