Identifier
Values
[.,.] => [1] => [1] => [1] => 0
[.,[.,.]] => [2,1] => [2,1] => [2,1] => 1
[[.,.],.] => [1,2] => [1,2] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => [3,2,1] => 2
[.,[[.,.],.]] => [2,3,1] => [3,1,2] => [3,1,2] => 2
[[.,.],[.,.]] => [3,1,2] => [2,3,1] => [2,3,1] => 2
[[.,[.,.]],.] => [2,1,3] => [1,3,2] => [1,3,2] => 1
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
[.,[.,[[.,.],.]]] => [3,4,2,1] => [4,1,3,2] => [4,1,3,2] => 3
[.,[[.,.],[.,.]]] => [4,2,3,1] => [3,4,2,1] => [3,4,2,1] => 3
[.,[[.,[.,.]],.]] => [3,2,4,1] => [4,3,1,2] => [4,3,1,2] => 3
[.,[[[.,.],.],.]] => [2,3,4,1] => [3,4,1,2] => [3,4,1,2] => 4
[[.,.],[.,[.,.]]] => [4,3,1,2] => [4,2,3,1] => [4,2,3,1] => 4
[[.,.],[[.,.],.]] => [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3
[[.,[.,.]],[.,.]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => 3
[[[.,.],.],[.,.]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => 3
[[.,[.,[.,.]]],.] => [3,2,1,4] => [1,4,3,2] => [1,4,3,2] => 2
[[.,[[.,.],.]],.] => [2,3,1,4] => [1,3,4,2] => [1,3,4,2] => 2
[[[.,.],[.,.]],.] => [3,1,2,4] => [1,4,2,3] => [1,4,2,3] => 2
[[[.,[.,.]],.],.] => [2,1,3,4] => [1,3,2,4] => [1,3,2,4] => 1
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [1,4,5,3,2] => [1,4,5,3,2] => 3
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [1,5,3,4,2] => [1,5,3,4,2] => 4
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [1,4,3,5,2] => [1,4,3,5,2] => 3
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [1,5,4,2,3] => [1,5,4,2,3] => 3
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [1,4,5,2,3] => [1,4,5,2,3] => 4
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [1,5,3,2,4] => [1,5,3,2,4] => 3
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,5,2,3,4] => [1,5,2,3,4] => 3
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 2
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [1,4,2,3,5] => [1,4,2,3,5] => 2
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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Description
The number of Bruhat lower covers of a permutation.
This is, for a signed permutation $\pi$, the number of signed permutations $\tau$ having a reduced word which is obtained by deleting a letter from a reduced word from $\pi$.
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
Tanimoto
Description
Add 1 to every entry of the permutation (n becomes 1 instead of n+1), except that when n appears at the front or the back of the permutation, instead remove it and place 1 at the other end of the permutation.
Map
to signed permutation
Description
The signed permutation with all signs positive.