Identifier
Values
[1,0] => [1,1,0,0] => [[2],[]] => 1
[1,0,1,0] => [1,1,0,1,0,0] => [[3],[]] => 1
[1,1,0,0] => [1,1,1,0,0,0] => [[2,2],[]] => 2
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [[4],[]] => 1
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [[3,3],[1]] => 2
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[3,2],[]] => 2
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [[2,2,2],[]] => 2
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [[3,3],[]] => 2
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [[5],[]] => 1
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => 2
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => 2
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => 2
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => 2
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => 2
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => 3
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => 2
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => 2
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => 2
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => 1
[] => [1,0] => [[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
click to show known generating functions       
Description
The Frobenius rank of a skew partition.
This is the minimal number of border strips in a border strip decomposition of the skew partition.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.