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
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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
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
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.