Identifier
Values
[1,2,3] => [1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 0
[1,3,2] => [1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 0
[2,1,3] => [1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 0
[2,3,1] => [1,2,3] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 0
[3,1,2] => [1,3,2] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 1
[3,2,1] => [1,3,2] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 1
[1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[1,2,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[1,3,2,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[1,3,4,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[1,4,2,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 1
[1,4,3,2] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 1
[2,1,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[2,1,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[2,3,1,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 0
[2,4,1,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 1
[2,4,3,1] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 1
[3,1,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[3,1,4,2] => [1,3,4,2] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0] => 0
[3,2,1,4] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[3,2,4,1] => [1,3,4,2] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0] => 0
[3,4,1,2] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[3,4,2,1] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[4,1,2,3] => [1,4,3,2] => [.,[[[.,.],.],.]] => [1,0,1,1,0,1,0,0] => 1
[4,1,3,2] => [1,4,2,3] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[4,2,1,3] => [1,4,3,2] => [.,[[[.,.],.],.]] => [1,0,1,1,0,1,0,0] => 1
[4,2,3,1] => [1,4,2,3] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[4,3,1,2] => [1,4,2,3] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[4,3,2,1] => [1,4,2,3] => [.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => 1
[1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,2,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,2,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,2,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,2,5,3,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,2,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,3,2,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,3,2,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,3,4,2,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,3,4,5,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,3,5,2,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,3,5,4,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,4,2,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,4,2,5,3] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,4,3,2,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,4,3,5,2] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,4,5,2,3] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,4,5,3,2] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,5,2,3,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,5,2,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,5,3,2,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,5,3,4,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,5,4,2,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,5,4,3,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,1,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,1,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,1,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,1,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,1,5,3,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[2,1,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[2,3,1,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,3,1,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,3,4,1,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,3,5,1,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[2,3,5,4,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[2,4,1,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,4,1,5,3] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,0,1,0] => 0
[2,4,3,1,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,4,3,5,1] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,0,1,0] => 0
[2,4,5,1,3] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,4,5,3,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,5,1,3,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,0,0] => 1
[2,5,1,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,5,3,1,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,0,0] => 1
[2,5,3,4,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,5,4,1,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,5,4,3,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[3,1,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,1,2,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,1,4,2,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[3,1,4,5,2] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,0,1,0] => 0
[3,1,5,2,4] => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,0,0] => 1
[3,1,5,4,2] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[3,2,1,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,2,1,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,2,4,1,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[3,2,4,5,1] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,0,1,0] => 0
[3,2,5,1,4] => [1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,0,0] => 1
[3,2,5,4,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[3,4,1,2,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,4,1,5,2] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,4,2,1,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,4,2,5,1] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,4,5,1,2] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[3,4,5,2,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[3,5,1,2,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[3,5,1,4,2] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[3,5,2,1,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[3,5,2,4,1] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[3,5,4,1,2] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
>>> Load all 150 entries. <<<
[3,5,4,2,1] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[4,1,2,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[4,1,2,5,3] => [1,4,5,3,2] => [.,[[[.,[.,.]],.],.]] => [1,0,1,1,0,1,0,0,1,0] => 0
[4,1,3,2,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,1,3,5,2] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[4,1,5,2,3] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,1,5,3,2] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 1
[4,2,1,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[4,2,1,5,3] => [1,4,5,3,2] => [.,[[[.,[.,.]],.],.]] => [1,0,1,1,0,1,0,0,1,0] => 0
[4,2,3,1,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,2,3,5,1] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[4,2,5,1,3] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,2,5,3,1] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 1
[4,3,1,2,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,3,1,5,2] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[4,3,2,1,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,3,2,5,1] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[4,3,5,1,2] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,3,5,2,1] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[4,5,1,2,3] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[4,5,1,3,2] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[4,5,2,1,3] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[4,5,2,3,1] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[4,5,3,1,2] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[4,5,3,2,1] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[5,1,2,3,4] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => 1
[5,1,2,4,3] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,1,3,2,4] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,1,3,4,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[5,1,4,2,3] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 1
[5,1,4,3,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[5,2,1,3,4] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => 1
[5,2,1,4,3] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,2,3,1,4] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,2,3,4,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[5,2,4,1,3] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 1
[5,2,4,3,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[5,3,1,2,4] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,3,1,4,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[5,3,2,1,4] => [1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,3,2,4,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[5,3,4,1,2] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[5,3,4,2,1] => [1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[5,4,1,2,3] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,4,1,3,2] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[5,4,2,1,3] => [1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,4,2,3,1] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[5,4,3,1,2] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[5,4,3,2,1] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => 1
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
click to show known generating functions       
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
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].