Identifier
Values
[1,0] => [2,1] => [1,2] => [1,2] => 0
[1,0,1,0] => [3,1,2] => [3,1,2] => [1,2,3] => 0
[1,1,0,0] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0] => [4,1,2,3] => [3,4,1,2] => [1,2,3,4] => 0
[1,0,1,1,0,0] => [3,1,4,2] => [3,1,2,4] => [1,2,4,3] => 1
[1,1,0,0,1,0] => [2,4,1,3] => [4,2,1,3] => [1,3,2,4] => 1
[1,1,0,1,0,0] => [4,3,1,2] => [4,1,3,2] => [1,3,2,4] => 1
[1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[] => [1] => [1] => [1] => 0
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Description
The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.