Identifier
Values
[1] => [1,0,1,0] => [1,1,0,0] => [1,1,1,0,0,0] => 1
[2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 2
[2,1] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 3
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[] => [] => [] => [1,0] => 1
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule.
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.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.