Identifier
Values
[.,.] => [1] => [1] => 0
[.,[.,.]] => [2,1] => [2,1] => 0
[[.,.],.] => [1,2] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => [2,3,1] => 0
[.,[[.,.],.]] => [2,3,1] => [3,2,1] => 0
[[.,.],[.,.]] => [3,1,2] => [1,3,2] => 1
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => 0
[[[.,.],.],.] => [1,2,3] => [1,2,3] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [3,4,2,1] => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => [4,3,2,1] => 0
[.,[[.,.],[.,.]]] => [4,2,3,1] => [2,4,3,1] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => [2,3,4,1] => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [3,2,4,1] => 0
[[.,.],[.,[.,.]]] => [4,3,1,2] => [3,4,1,2] => 0
[[.,.],[[.,.],.]] => [3,4,1,2] => [4,3,1,2] => 0
[[.,[.,.]],[.,.]] => [4,2,1,3] => [2,4,1,3] => 1
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,4,2,3] => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => [2,3,1,4] => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => [3,2,1,4] => 0
[[[.,.],[.,.]],.] => [3,1,2,4] => [1,3,2,4] => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => 0
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [4,5,3,2,1] => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [5,4,3,2,1] => 0
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [3,5,4,2,1] => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [3,4,5,2,1] => 0
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [4,3,5,2,1] => 0
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [4,5,2,3,1] => 0
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [5,4,2,3,1] => 0
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [3,5,2,4,1] => 1
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [2,5,3,4,1] => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [3,4,2,5,1] => 0
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [4,3,2,5,1] => 0
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [2,4,3,5,1] => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [2,3,4,5,1] => 0
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [3,2,4,5,1] => 0
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [4,5,3,1,2] => 0
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [5,4,3,1,2] => 0
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [3,5,4,1,2] => 1
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [3,4,5,1,2] => 0
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [4,3,5,1,2] => 0
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [4,5,2,1,3] => 0
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [5,4,2,1,3] => 0
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [4,5,1,2,3] => 0
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [5,4,1,2,3] => 0
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [3,5,2,1,4] => 1
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [2,5,3,1,4] => 1
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [3,5,1,2,4] => 1
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [2,5,1,3,4] => 1
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,5,2,3,4] => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [3,4,2,1,5] => 0
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [4,3,2,1,5] => 0
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [2,4,3,1,5] => 1
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [2,3,4,1,5] => 0
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [3,2,4,1,5] => 0
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [3,4,1,2,5] => 0
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [4,3,1,2,5] => 0
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [2,4,1,3,5] => 1
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,4,2,3,5] => 1
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [2,3,1,4,5] => 0
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,2,1,4,5] => 0
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [1,3,2,4,5] => 1
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => 0
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [5,6,4,3,2,1] => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [6,5,4,3,2,1] => 0
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [4,6,5,3,2,1] => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [4,5,6,3,2,1] => 0
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [5,4,6,3,2,1] => 0
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [5,6,3,4,2,1] => 0
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [6,5,3,4,2,1] => 0
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => 1
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [3,6,4,5,2,1] => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [4,5,3,6,2,1] => 0
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [5,4,3,6,2,1] => 0
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [3,5,4,6,2,1] => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [3,4,5,6,2,1] => 0
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [4,3,5,6,2,1] => 0
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [5,6,4,2,3,1] => 0
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [6,5,4,2,3,1] => 0
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [4,6,5,2,3,1] => 1
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [4,5,6,2,3,1] => 0
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [5,4,6,2,3,1] => 0
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [5,6,3,2,4,1] => 0
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [6,5,3,2,4,1] => 0
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [5,6,2,3,4,1] => 0
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [6,5,2,3,4,1] => 0
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => 1
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [3,6,4,2,5,1] => 1
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [4,6,2,3,5,1] => 1
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [3,6,2,4,5,1] => 1
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [2,6,3,4,5,1] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [4,5,3,2,6,1] => 0
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [5,4,3,2,6,1] => 0
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [3,4,5,2,6,1] => 0
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [4,3,5,2,6,1] => 0
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [4,5,2,3,6,1] => 0
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [5,4,2,3,6,1] => 0
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => 1
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [2,5,3,4,6,1] => 1
>>> Load all 199 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [3,4,2,5,6,1] => 0
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [4,3,2,5,6,1] => 0
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => 1
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [2,3,4,5,6,1] => 0
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [3,2,4,5,6,1] => 0
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [5,6,4,3,1,2] => 0
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [6,5,4,3,1,2] => 0
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [4,6,5,3,1,2] => 1
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [4,5,6,3,1,2] => 0
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [5,4,6,3,1,2] => 0
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [5,6,3,4,1,2] => 0
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [6,5,3,4,1,2] => 0
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [4,6,3,5,1,2] => 1
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [3,6,4,5,1,2] => 1
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [4,5,3,6,1,2] => 0
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [5,4,3,6,1,2] => 0
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [3,5,4,6,1,2] => 1
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [3,4,5,6,1,2] => 0
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [4,3,5,6,1,2] => 0
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [5,6,4,2,1,3] => 0
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [6,5,4,2,1,3] => 0
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [4,6,5,2,1,3] => 1
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [4,5,6,2,1,3] => 0
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [5,4,6,2,1,3] => 0
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [5,6,4,1,2,3] => 0
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [6,5,4,1,2,3] => 0
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [4,6,5,1,2,3] => 1
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [4,5,6,1,2,3] => 0
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [5,4,6,1,2,3] => 0
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [5,6,3,2,1,4] => 0
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [6,5,3,2,1,4] => 0
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [5,6,2,3,1,4] => 0
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [6,5,2,3,1,4] => 0
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [5,6,3,1,2,4] => 0
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [6,5,3,1,2,4] => 0
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [5,6,2,1,3,4] => 0
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [6,5,2,1,3,4] => 0
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [5,6,1,2,3,4] => 0
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [6,5,1,2,3,4] => 0
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [4,6,3,2,1,5] => 1
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [3,6,4,2,1,5] => 1
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [4,6,2,3,1,5] => 1
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [3,6,2,4,1,5] => 1
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [2,6,3,4,1,5] => 1
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [4,6,3,1,2,5] => 1
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [3,6,4,1,2,5] => 1
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [4,6,2,1,3,5] => 1
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [4,6,1,2,3,5] => 1
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [3,6,2,1,4,5] => 1
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [2,6,3,1,4,5] => 1
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [3,6,1,2,4,5] => 1
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => 1
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,6,2,3,4,5] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [4,5,3,2,1,6] => 0
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [5,4,3,2,1,6] => 0
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => 1
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [3,4,5,2,1,6] => 0
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [4,3,5,2,1,6] => 0
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [4,5,2,3,1,6] => 0
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [5,4,2,3,1,6] => 0
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => 1
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [2,5,3,4,1,6] => 1
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [3,4,2,5,1,6] => 0
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [4,3,2,5,1,6] => 0
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => 1
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [2,3,4,5,1,6] => 0
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [3,2,4,5,1,6] => 0
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [4,5,3,1,2,6] => 0
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [5,4,3,1,2,6] => 0
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [3,5,4,1,2,6] => 1
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [3,4,5,1,2,6] => 0
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [4,3,5,1,2,6] => 0
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [4,5,2,1,3,6] => 0
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [5,4,2,1,3,6] => 0
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [4,5,1,2,3,6] => 0
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [5,4,1,2,3,6] => 0
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [3,5,2,1,4,6] => 1
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [2,5,3,1,4,6] => 1
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [3,5,1,2,4,6] => 1
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => 1
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [1,5,2,3,4,6] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [3,4,2,1,5,6] => 0
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [4,3,2,1,5,6] => 0
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => 1
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [2,3,4,1,5,6] => 0
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [3,2,4,1,5,6] => 0
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [3,4,1,2,5,6] => 0
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [4,3,1,2,5,6] => 0
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => 1
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [1,4,2,3,5,6] => 1
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 0
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => 0
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => 1
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 0
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [1,4,2,3,5,6,7] => 1
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
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Description
The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation.
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.
Map
Alexandersson Kebede
Description
Sends a permutation to a permutation and it preserves the set of right-to-left minima.
Take a permutation $\pi$ of length $n$. The mapping looks for a smallest odd integer $i\in[n-1]$ such that swapping the entries $\pi(i)$ and $\pi(i+1)$ preserves the set of right-to-left minima. Otherwise, $\pi$ will be a fixed element of the mapping. Note that the map changes the sign of all non-fixed elements.
There are exactly $\binom{\lfloor n/2 \rfloor}{k-\lceil n/2 \rceil}$ elements in $S_n$ fixed under this map, with exactly $k$ right-to-left minima, see Lemma 35 in [1].