Identifier
Values
[[1]] => [1] => [1,0,1,0] => [3,1,2] => 1
[[1,2]] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 1
[[1],[2]] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 1
[[1,2,3]] => [3] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 1
[[1,3],[2]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[1,2],[3]] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[[1],[2],[3]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[[1,3,4],[2]] => [3,1] => [1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 1
[[1,2,4],[3]] => [3,1] => [1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 1
[[1,2,3],[4]] => [3,1] => [1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 1
[[1,3],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 1
[[1,2],[3,4]] => [2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 1
[[1,4],[2],[3]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[[1,3],[2],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[[1,2],[3],[4]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[[1,3,5],[2,4]] => [3,2] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 1
[[1,2,5],[3,4]] => [3,2] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 1
[[1,3,4],[2,5]] => [3,2] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 1
[[1,2,4],[3,5]] => [3,2] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 1
[[1,2,3],[4,5]] => [3,2] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 1
[[1,4,5],[2],[3]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 1
[[1,3,5],[2],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 1
[[1,2,5],[3],[4]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 1
[[1,3,4],[2],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 1
[[1,2,4],[3],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 1
[[1,2,3],[4],[5]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 1
[[1,4],[2,5],[3]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[[1,3],[2,5],[4]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[[1,2],[3,5],[4]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[[1,3],[2,4],[5]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[[1,2],[3,4],[5]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[[1,4,6],[2,5],[3]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,3,6],[2,5],[4]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,2,6],[3,5],[4]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,3,6],[2,4],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,2,6],[3,4],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,4,5],[2,6],[3]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,3,5],[2,6],[4]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,2,5],[3,6],[4]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,3,4],[2,6],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,2,4],[3,6],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,2,3],[4,6],[5]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,3,5],[2,4],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,2,5],[3,4],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,3,4],[2,5],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,2,4],[3,5],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[[1,2,3],[4,5],[6]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 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 number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$.
Map
shape
Description
Sends a tableau to its shape.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.