Identifier
Values
[1,0] => [1] => 1
[1,0,1,0] => [1,1] => 2
[1,1,0,0] => [2] => 1
[1,0,1,0,1,0] => [1,1,1] => 3
[1,0,1,1,0,0] => [1,2] => 2
[1,1,0,0,1,0] => [2,1] => 2
[1,1,0,1,0,0] => [2,1] => 2
[1,1,1,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1] => 4
[1,0,1,0,1,1,0,0] => [1,1,2] => 3
[1,0,1,1,0,0,1,0] => [1,2,1] => 2
[1,0,1,1,0,1,0,0] => [1,2,1] => 2
[1,0,1,1,1,0,0,0] => [1,3] => 2
[1,1,0,0,1,0,1,0] => [2,1,1] => 3
[1,1,0,0,1,1,0,0] => [2,2] => 2
[1,1,0,1,0,0,1,0] => [2,1,1] => 3
[1,1,0,1,0,1,0,0] => [2,1,1] => 3
[1,1,0,1,1,0,0,0] => [2,2] => 2
[1,1,1,0,0,0,1,0] => [3,1] => 2
[1,1,1,0,0,1,0,0] => [3,1] => 2
[1,1,1,0,1,0,0,0] => [3,1] => 2
[1,1,1,1,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 3
[1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 3
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,2,2] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,4] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,3] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => 4
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => 3
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => 4
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,2,1] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,2,1] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,2,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,3] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,2] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => 3
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => 3
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => 3
[1,1,1,0,1,1,0,0,0,0] => [3,2] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,1] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,1] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,1] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,1] => 2
[1,1,1,1,1,0,0,0,0,0] => [5] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => 2
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,4] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => 1
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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
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.