Identifier
Values
00 => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
11 => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
000 => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
111 => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
0000 => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
1111 => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
00000 => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
11111 => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
000000 => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
111111 => [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
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Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
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
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 composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.