Identifier
Values
[1,1] => [[1,1],[]] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 0
[2] => [[2],[]] => ([(0,1)],2) => ([(0,2),(2,1)],3) => 0
[1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 0
[1,2] => [[2,1],[]] => ([(0,1),(0,2)],3) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[2,1] => [[2,2],[1]] => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[3] => [[3],[]] => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,2] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[1,3] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[2,1,1] => [[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[3,1] => [[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
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
Number of indecomposable injective modules with projective dimension 2.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
Map
order ideals
Description
The lattice of order ideals of a poset.
An order ideal $\mathcal I$ in a poset $P$ is a downward closed set, i.e., $a \in \mathcal I$ and $b \leq a$ implies $b \in \mathcal I$. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
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.