Identifier
Values
[1] => [1,0,1,0] => [1,1] => 2
[2] => [1,1,0,0,1,0] => [2,1] => 2
[1,1] => [1,0,1,1,0,0] => [1,2] => 2
[3] => [1,1,1,0,0,0,1,0] => [3,1] => 2
[2,1] => [1,0,1,0,1,0] => [1,1,1] => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,3] => 2
[4] => [1,1,1,1,0,0,0,0,1,0] => [4,1] => 2
[3,1] => [1,1,0,1,0,0,1,0] => [3,1] => 2
[2,2] => [1,1,0,0,1,1,0,0] => [2,2] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,3] => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,4] => 2
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => 2
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 2
[3,2] => [1,1,0,0,1,0,1,0] => [2,1,1] => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,2,1] => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,2] => 3
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,4] => 2
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 2
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 2
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [4,1] => 2
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [4,1] => 2
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => 4
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4] => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,3] => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,4] => 2
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => 2
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => 2
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => 2
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 3
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [4,1] => 2
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 2
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,2] => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,3] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,4] => 2
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 3
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => 2
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => 2
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => 2
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => 2
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => 2
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,1] => 3
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,1] => 2
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => 2
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 3
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 2
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3] => 3
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => 2
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => 3
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => 2
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => 2
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => 2
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 4
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 3
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 3
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 4
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => 2
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 3
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => 3
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => 2
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => 2
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => 2
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => 2
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => 2
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => 5
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => 2
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => 2
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => 2
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => 2
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => 2
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => 3
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => 3
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => 3
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 2
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => 2
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => 2
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => 2
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 3
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 2
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => 3
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 3
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 2
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => 3
>>> Load all 131 entries. <<<
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 4
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => 3
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 3
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => 2
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => 2
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => 2
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 3
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => 3
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => 2
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => 2
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => 3
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => 2
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => 3
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 4
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => 4
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => 3
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => 3
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 3
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 2
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => 3
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => 4
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 3
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => 3
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => 4
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => 5
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 4
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 4
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 5
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 6
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Description
The global dimension of the corresponding Comp-Nakayama algebra.
We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.