Identifier
Values
=>
Cc0028;cc-rep-2 Cc0014;cc-rep
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
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.
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.