Identifier
Values
[1,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[3,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[2,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[4,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[4,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[3,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[5,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[5,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[4,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,1,1,1,1,1,1,1] => [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
[6,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[6,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[5,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[3,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,1,1,1,1,1,1,1] => [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
[7,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[7,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[6,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[6,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[6,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[5,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[4,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[4,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[3,1,1,1,1,1,1,1] => [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
[8,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[8,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[7,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[7,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[7,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[6,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[6,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[5,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[5,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[4,1,1,1,1,1,1,1] => [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
[9,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[9,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[8,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[8,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[8,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[7,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[7,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[6,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[6,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[6,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[5,1,1,1,1,1,1,1] => [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
[10,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[10,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[9,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[9,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[9,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[8,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[8,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[7,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[7,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[7,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[6,1,1,1,1,1,1,1] => [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
[11,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[11,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[10,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[10,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[10,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[9,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[9,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[8,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[8,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[8,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[7,7] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[7,1,1,1,1,1,1,1] => [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
[12,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[12,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[11,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[11,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[11,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[10,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[10,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[9,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[9,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
>>> Load all 131 entries. <<<
[9,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[8,7] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[8,1,1,1,1,1,1,1] => [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
[13,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[13,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[12,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[12,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[12,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[11,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[11,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[10,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[10,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[10,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[9,7] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[9,1,1,1,1,1,1,1] => [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
[14,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[14,1,1,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[13,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[13,2,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[13,1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[12,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[12,1,1,1,1,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[11,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[11,3,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[11,2,2,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[10,7] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[10,1,1,1,1,1,1,1] => [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
first row removal
Description
Removes the first entry of an integer partition
Map
to skew partition
Description
The partition regarded as a skew partition.
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.