Identifier
Values
[1,0] => [1,0] => [.,.] => [1,0] => 0
[1,0,1,0] => [1,1,0,0] => [[.,.],.] => [1,1,0,0] => 0
[1,1,0,0] => [1,0,1,0] => [.,[.,.]] => [1,0,1,0] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [[[.,.],.],.] => [1,1,0,1,0,0] => 2
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [[.,.],[.,.]] => [1,1,1,0,0,0] => 0
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 2
[1,1,0,1,0,0] => [1,1,0,1,0,0] => [[.,[.,.]],.] => [1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => [1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],.] => [1,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => [1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],.] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,.]] => [1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],.] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[.,.]] => [1,1,1,0,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],.]],.] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0] => 9
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[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] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[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] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 12
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[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] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[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] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
>>> Load all 127 entries. <<<
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 9
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
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 number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
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].