Identifier
Values
[1] => [1] => [1,0] => [2,1] => 1
[1,2] => [2] => [1,0,1,0] => [3,1,2] => 1
[2,1] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[1,2,3] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[1,3,2] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 1
[2,1,3] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 1
[2,3,1] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 1
[3,1,2] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 1
[3,2,1] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 1
[1,2,3,4] => [4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[1,2,4,3] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[1,3,2,4] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[1,3,4,2] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[1,4,2,3] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[1,4,3,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[2,1,3,4] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[2,1,4,3] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[2,3,1,4] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[2,3,4,1] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[2,4,1,3] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[2,4,3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[3,1,2,4] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[3,1,4,2] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[3,2,1,4] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[3,2,4,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[3,4,1,2] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[3,4,2,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[4,1,2,3] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[4,1,3,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[4,2,1,3] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[4,2,3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[4,3,1,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[4,3,2,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 1
[1,3,2,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[1,3,5,2,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[1,4,2,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[1,4,5,2,3] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,1,3,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,1,4,3,5] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,1,4,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,1,5,3,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,1,5,4,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[2,3,1,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,3,5,1,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,4,1,3,5] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,4,1,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,4,5,1,3] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,5,1,3,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[2,5,1,4,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[2,5,4,1,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[3,1,2,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[3,1,4,2,5] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[3,1,4,5,2] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[3,1,5,2,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[3,1,5,4,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[3,2,1,5,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[3,2,5,1,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[3,2,5,4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[3,4,1,2,5] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[3,4,1,5,2] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[3,4,5,1,2] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[3,5,1,2,4] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[3,5,1,4,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[3,5,2,1,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[3,5,2,4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[3,5,4,1,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,1,2,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[4,1,5,2,3] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[4,1,5,3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,2,1,5,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,2,5,1,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,2,5,3,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,3,1,5,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,3,5,1,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,5,1,2,3] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[4,5,1,3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,5,2,1,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,5,2,3,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[4,5,3,1,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[5,2,1,4,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[5,2,4,1,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[5,3,1,4,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[5,3,4,1,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[2,1,4,3,6,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,1,4,6,3,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,1,5,3,6,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,1,5,6,3,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,4,1,3,6,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,4,1,6,3,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,4,6,1,3,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,5,1,3,6,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,5,1,6,3,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[2,5,6,1,3,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,1,4,2,6,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,1,4,6,2,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,1,5,2,6,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,1,5,6,2,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,2,1,6,5,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[3,2,6,1,5,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[3,2,6,5,1,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[3,4,1,2,6,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
>>> Load all 134 entries. <<<
[3,4,1,6,2,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,4,6,1,2,5] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,5,1,2,6,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,5,1,6,2,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,5,6,1,2,4] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[3,6,2,1,5,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[3,6,2,5,1,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,1,5,2,6,3] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[4,1,5,6,2,3] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[4,2,1,6,5,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,2,6,1,5,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,2,6,5,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,3,1,6,5,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,3,6,1,5,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,3,6,5,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,5,1,2,6,3] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[4,5,1,6,2,3] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[4,5,6,1,2,3] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[4,6,2,1,5,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,6,2,5,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,6,3,1,5,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[4,6,3,5,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,2,1,6,4,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,2,6,1,4,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,2,6,4,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,3,1,6,4,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,3,6,1,4,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,3,6,4,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,6,2,1,4,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,6,2,4,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,6,3,1,4,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5,6,3,4,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[] => [] => [] => [1] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
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
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
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
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.