Identifier
Values
0 => [2] => [1,1,0,0] => [2,3,1] => 2
1 => [1,1] => [1,0,1,0] => [3,1,2] => 2
00 => [3] => [1,1,1,0,0,0] => [2,3,4,1] => 3
01 => [2,1] => [1,1,0,0,1,0] => [2,4,1,3] => 2
10 => [1,2] => [1,0,1,1,0,0] => [3,1,4,2] => 2
11 => [1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
=> [1] => [1,0] => [2,1] => 1
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Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
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
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.