Identifier
Values
[.,.] => [1] => 1
[.,[.,.]] => [2,1] => 1
[[.,.],.] => [1,2] => 1
[.,[.,[.,.]]] => [3,2,1] => 1
[.,[[.,.],.]] => [2,3,1] => 1
[[.,.],[.,.]] => [1,3,2] => 1
[[.,[.,.]],.] => [2,1,3] => 1
[[[.,.],.],.] => [1,2,3] => 1
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 1
[.,[.,[[.,.],.]]] => [3,4,2,1] => 1
[.,[[.,.],[.,.]]] => [2,4,3,1] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => 1
[.,[[[.,.],.],.]] => [2,3,4,1] => 1
[[.,.],[.,[.,.]]] => [1,4,3,2] => 1
[[.,.],[[.,.],.]] => [1,3,4,2] => 1
[[.,[.,.]],[.,.]] => [2,1,4,3] => 2
[[[.,.],.],[.,.]] => [1,2,4,3] => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => 1
[[.,[[.,.],.]],.] => [2,3,1,4] => 1
[[[.,.],[.,.]],.] => [1,3,2,4] => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => 1
[[[[.,.],.],.],.] => [1,2,3,4] => 1
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 1
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 1
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 1
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 1
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 1
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 1
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 1
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 1
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 1
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 1
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 2
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 2
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 1
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 1
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 2
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 2
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 2
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 2
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 1
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 1
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 1
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 1
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 1
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 1
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 2
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 1
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 1
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 1
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 1
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Description
The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$.
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.