Identifier
-
Mp00230:
Integer partitions
—parallelogram polyomino⟶
Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St000964: Dyck paths ⟶ ℤ
Values
[1] => [1,0] => [1,1,0,0] => 3
[2] => [1,0,1,0] => [1,1,0,1,0,0] => 3
[1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 6
[3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 6
[4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 3
[3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 10
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 3
[3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 3
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 4
[2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 6
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 10
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 15
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 3
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 3
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 10
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 15
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 21
[] => [] => [1,0] => 1
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Description
Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra.
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.
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
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
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