Identifier
-
Mp00083:
Standard tableaux
—shape⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001195: Dyck paths ⟶ ℤ
Values
[[1]] => [1] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[[1,2]] => [2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 1
[[1],[2]] => [1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 1
[[1,2,3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[[1,3],[2]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[[1,2],[3]] => [2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[[1],[2],[3]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[[1,3,4],[2]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[[1,2,4],[3]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[[1,2,3],[4]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[[1,3],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,2],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[[1,4],[2],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[[1,3],[2],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[[1,2],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[[1,3,5],[2,4]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[[1,2,5],[3,4]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[[1,3,4],[2,5]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[[1,2,4],[3,5]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[[1,2,3],[4,5]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[[1,4,5],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[[1,3,5],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[[1,2,5],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[[1,3,4],[2],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[[1,2,4],[3],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[[1,2,3],[4],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[[1,4],[2,5],[3]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[[1,3],[2,5],[4]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[[1,2],[3,5],[4]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[[1,3],[2,4],[5]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[[1,2],[3,4],[5]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[[1,4,6],[2,5],[3]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,3,6],[2,5],[4]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,2,6],[3,5],[4]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,3,6],[2,4],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,2,6],[3,4],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,4,5],[2,6],[3]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,3,5],[2,6],[4]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,2,5],[3,6],[4]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,3,4],[2,6],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,2,4],[3,6],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,2,3],[4,6],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,3,5],[2,4],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,2,5],[3,4],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,3,4],[2,5],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,2,4],[3,5],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[1,2,3],[4,5],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 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
shape
Description
Sends a tableau to its shape.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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