Identifier
Values
[.,.] => [1] => [1] => [1] => 1
[.,[.,.]] => [2,1] => [1,2] => [1,2] => 2
[[.,.],.] => [1,2] => [1,2] => [1,2] => 2
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => [1,2,3] => 3
[.,[[.,.],.]] => [2,3,1] => [1,2,3] => [1,2,3] => 3
[[.,.],[.,.]] => [3,1,2] => [1,2,3] => [1,2,3] => 3
[[.,[.,.]],.] => [2,1,3] => [1,3,2] => [1,3,2] => 2
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,2,3] => 3
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 4
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,3,4] => [1,2,3,4] => 4
[.,[[.,.],[.,.]]] => [4,2,3,1] => [1,2,3,4] => [1,2,3,4] => 4
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,2,4,3] => [1,2,4,3] => 3
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 4
[[.,.],[.,[.,.]]] => [4,3,1,2] => [1,2,3,4] => [1,2,3,4] => 4
[[.,.],[[.,.],.]] => [3,4,1,2] => [1,2,3,4] => [1,2,3,4] => 4
[[.,[.,.]],[.,.]] => [4,2,1,3] => [1,3,2,4] => [1,3,2,4] => 3
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,3,4] => [1,2,3,4] => 4
[[.,[.,[.,.]]],.] => [3,2,1,4] => [1,4,2,3] => [1,4,2,3] => 3
[[.,[[.,.],.]],.] => [2,3,1,4] => [1,4,2,3] => [1,4,2,3] => 3
[[[.,.],[.,.]],.] => [3,1,2,4] => [1,2,4,3] => [1,2,4,3] => 3
[[[.,[.,.]],.],.] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => 3
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4
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Description
The number of minimal elements in Bruhat order not less than the signed permutation.
The minimal elements in question are biGrassmannian, that is both the element and its inverse have at most one descent.
This is the size of the essential set of the signed permutation, see [1].
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
to signed permutation
Description
The signed permutation with all signs positive.
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.