Identifier
Values
[1,2] => [.,[.,.]] => [2,1] => 1
[2,1] => [[.,.],.] => [1,2] => 0
[1,2,3] => [.,[.,[.,.]]] => [3,2,1] => 2
[1,3,2] => [.,[[.,.],.]] => [2,3,1] => 2
[2,1,3] => [[.,.],[.,.]] => [1,3,2] => 1
[2,3,1] => [[.,.],[.,.]] => [1,3,2] => 1
[3,1,2] => [[.,[.,.]],.] => [2,1,3] => 1
[3,2,1] => [[[.,.],.],.] => [1,2,3] => 0
[1,2,3,4] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 3
[1,2,4,3] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 3
[1,3,2,4] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 3
[1,3,4,2] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 3
[1,4,2,3] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 3
[1,4,3,2] => [.,[[[.,.],.],.]] => [2,3,4,1] => 3
[2,1,3,4] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 2
[2,1,4,3] => [[.,.],[[.,.],.]] => [1,3,4,2] => 2
[2,3,1,4] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 2
[2,3,4,1] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 2
[2,4,1,3] => [[.,.],[[.,.],.]] => [1,3,4,2] => 2
[2,4,3,1] => [[.,.],[[.,.],.]] => [1,3,4,2] => 2
[3,1,2,4] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 1
[3,1,4,2] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 1
[3,2,1,4] => [[[.,.],.],[.,.]] => [1,2,4,3] => 1
[3,2,4,1] => [[[.,.],.],[.,.]] => [1,2,4,3] => 1
[3,4,1,2] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 1
[3,4,2,1] => [[[.,.],.],[.,.]] => [1,2,4,3] => 1
[4,1,2,3] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 2
[4,1,3,2] => [[.,[[.,.],.]],.] => [2,3,1,4] => 2
[4,2,1,3] => [[[.,.],[.,.]],.] => [1,3,2,4] => 1
[4,2,3,1] => [[[.,.],[.,.]],.] => [1,3,2,4] => 1
[4,3,1,2] => [[[.,[.,.]],.],.] => [2,1,3,4] => 1
[4,3,2,1] => [[[[.,.],.],.],.] => [1,2,3,4] => 0
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Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 312-avoiding permutation
Description
Return a 312-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 minimal element of this Sylvester class.