Identifier
Values
[3] => [2,1] => [1,0,1,1,0,0] => 1
[2,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1] => [3] => [1,0,1,0,1,0] => 0
[4] => [2,2] => [1,1,1,0,0,0] => 1
[3,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[2,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1] => [4] => [1,0,1,0,1,0,1,0] => 0
[5] => [3,2] => [1,0,1,1,1,0,0,0] => 1
[4,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[3,2] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[3,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
[2,1,1,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[6] => [3,3] => [1,1,1,0,1,0,0,0] => 1
[5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
[4,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1
[2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[7] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[2,2,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[8] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[5,1,1,1] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,2,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,2,2,2,1] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
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Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
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.
Map
Loehr-Warrington inverse
Description
Return a partition whose length is the diagonal inversion number of the preimage.