Identifier
Values
[1] => [1,0] => 2
[2] => [1,0,1,0] => 2
[1,1] => [1,1,0,0] => 3
[3] => [1,0,1,0,1,0] => 2
[2,1] => [1,0,1,1,0,0] => 3
[1,1,1] => [1,1,0,1,0,0] => 2
[4] => [1,0,1,0,1,0,1,0] => 2
[3,1] => [1,0,1,0,1,1,0,0] => 3
[2,2] => [1,1,1,0,0,0] => 4
[2,1,1] => [1,0,1,1,0,1,0,0] => 2
[1,1,1,1] => [1,1,0,1,0,1,0,0] => 2
[5] => [1,0,1,0,1,0,1,0,1,0] => 2
[4,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[3,2] => [1,0,1,1,1,0,0,0] => 4
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[2,2,1] => [1,1,1,0,0,1,0,0] => 3
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 2
[6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
[5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[3,3] => [1,1,1,0,1,0,0,0] => 2
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[2,2,2] => [1,1,1,1,0,0,0,0] => 5
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[4,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 5
[3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 4
[2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[4,4] => [1,1,1,0,1,0,1,0,0,0] => 2
[4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 5
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
[3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 4
[3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
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Description
The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra.
That is the number of i such that $Ext_A^1(J,e_i J)=0$.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.