Identifier
Values
[1] => [[1],[]] => [[1],[]] => ([],1) => 0
[2] => [[2],[]] => [[2],[]] => ([(0,1)],2) => 0
[1,1] => [[1,1],[]] => [[1,1],[]] => ([(0,1)],2) => 0
[3] => [[3],[]] => [[3],[]] => ([(0,2),(2,1)],3) => 0
[2,1] => [[2,1],[]] => [[2,2],[1]] => ([(0,2),(1,2)],3) => 0
[1,1,1] => [[1,1,1],[]] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 0
[4] => [[4],[]] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 0
[3,1] => [[3,1],[]] => [[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => 0
[2,2] => [[2,2],[]] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[2,1,1] => [[2,1,1],[]] => [[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => 0
[1,1,1,1] => [[1,1,1,1],[]] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 0
[5] => [[5],[]] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,1] => [[4,1],[]] => [[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
[3,2] => [[3,2],[]] => [[3,3],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1
[3,1,1] => [[3,1,1],[]] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
[2,2,1] => [[2,2,1],[]] => [[2,2,2],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1
[2,1,1,1] => [[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
[1,1,1,1,1] => [[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[6] => [[6],[]] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,1] => [[5,1],[]] => [[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
[4,1,1] => [[4,1,1],[]] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[3,2,1] => [[3,2,1],[]] => [[3,3,3],[2,1]] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 2
[3,1,1,1] => [[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[2,1,1,1,1] => [[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
[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) => 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
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Map
rotate
Description
The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.
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.