Identifier
Values
[.,.] => [1] => 1
[.,[.,.]] => [2,1] => 1
[[.,.],.] => [1,2] => 2
[.,[.,[.,.]]] => [3,2,1] => 1
[.,[[.,.],.]] => [2,3,1] => 1
[[.,.],[.,.]] => [3,1,2] => 2
[[.,[.,.]],.] => [2,1,3] => 2
[[[.,.],.],.] => [1,2,3] => 3
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 1
[.,[.,[[.,.],.]]] => [3,4,2,1] => 1
[.,[[.,.],[.,.]]] => [4,2,3,1] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => 1
[.,[[[.,.],.],.]] => [2,3,4,1] => 1
[[.,.],[.,[.,.]]] => [4,3,1,2] => 2
[[.,.],[[.,.],.]] => [3,4,1,2] => 2
[[.,[.,.]],[.,.]] => [4,2,1,3] => 2
[[[.,.],.],[.,.]] => [4,1,2,3] => 3
[[.,[.,[.,.]]],.] => [3,2,1,4] => 2
[[.,[[.,.],.]],.] => [2,3,1,4] => 2
[[[.,.],[.,.]],.] => [3,1,2,4] => 3
[[[.,[.,.]],.],.] => [2,1,3,4] => 3
[[[[.,.],.],.],.] => [1,2,3,4] => 4
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => 1
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => 1
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => 1
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 1
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 1
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 1
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => 2
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => 2
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => 2
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => 2
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => 2
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => 2
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => 2
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => 3
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => 3
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => 2
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => 2
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => 3
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => 3
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => 4
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 2
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 2
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => 2
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 2
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 2
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => 3
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => 3
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => 3
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => 4
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 3
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 3
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => 4
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 4
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 5
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 1
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => 1
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => 1
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 1
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 1
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => 1
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => 1
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => 1
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => 1
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => 1
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => 1
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => 1
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => 1
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => 1
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => 1
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => 1
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 1
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 1
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 1
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => 1
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => 1
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => 1
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => 1
>>> Load all 196 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 1
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 1
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => 1
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 1
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => 2
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => 2
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => 2
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => 2
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => 2
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => 2
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => 2
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => 2
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => 2
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => 2
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => 2
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => 3
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => 3
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => 3
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => 3
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => 2
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => 2
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => 3
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => 3
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => 3
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => 4
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => 4
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => 2
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => 2
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => 3
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => 3
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => 4
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => 3
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => 3
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => 4
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => 4
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => 5
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 2
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 2
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 2
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => 2
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => 2
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => 2
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => 2
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 2
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 2
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => 2
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 2
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 2
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => 3
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => 3
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => 3
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => 3
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => 3
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => 3
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => 3
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => 4
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => 4
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => 3
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => 3
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => 4
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => 4
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => 5
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 3
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 3
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => 3
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 3
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 3
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => 4
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => 4
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => 4
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => 5
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 4
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 4
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => 5
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 5
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 6
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Description
The number of right-to-left minima of a permutation.
For the number of left-to-right maxima, see St000314The number of left-to-right-maxima of 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.