Identifier
Values
{{1,2,3}} => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
{{1},{2},{3}} => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
{{1,2,3,4}} => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
{{1,2},{3,4}} => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
{{1,3},{2,4}} => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
{{1,4},{2,3}} => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
{{1},{2},{3},{4}} => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
{{1,2,3,4,5}} => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
{{1,2,3,4,5,6}} => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
{{1,2,3},{4,5,6}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,2,4},{3,5,6}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,2,5},{3,4,6}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,2,6},{3,4,5}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,2},{3,4},{5,6}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,2},{3,5},{4,6}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,2},{3,6},{4,5}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,3,4},{2,5,6}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,3,5},{2,4,6}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,3,6},{2,4,5}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,3},{2,4},{5,6}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,3},{2,5},{4,6}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,3},{2,6},{4,5}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,4,5},{2,3,6}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,4,6},{2,3,5}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,4},{2,3},{5,6}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,5,6},{2,3,4}} => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,5},{2,3},{4,6}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,6},{2,3},{4,5}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,4},{2,5},{3,6}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,4},{2,6},{3,5}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,5},{2,4},{3,6}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,6},{2,4},{3,5}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,5},{2,6},{3,4}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1,6},{2,5},{3,4}} => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
{{1,2,3,4,5,6,7}} => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
search for individual values
searching the database for the individual values of this statistic
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.
Map
to skew partition
Description
The partition regarded as a skew partition.
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.