Identifier
Values
([2],3) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 5
([1,1],3) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 5
([2],4) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 5
([1,1],4) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 5
([2,1],4) => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 6
([2],5) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 5
([1,1],5) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 5
([2,1],5) => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 6
([2],6) => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 5
([1,1],6) => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 5
([2,1],6) => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 6
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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
to partition
Description
Considers a core as a partition.
This embedding is graded and injective but not surjective on $k$-cores for a given parameter $k$, while it is surjective and neither graded nor injective on the collection of all cores.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.