Identifier
Values
[1] => [1,0,1,0] => 2
[2] => [1,1,0,0,1,0] => 2
[1,1] => [1,0,1,1,0,0] => 1
[3] => [1,1,1,0,0,0,1,0] => 2
[2,1] => [1,0,1,0,1,0] => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,1] => [1,1,0,1,0,0,1,0] => 3
[2,2] => [1,1,0,0,1,1,0,0] => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[4,1] => [1,1,1,0,1,0,0,0,1,0] => 3
[3,2] => [1,1,0,0,1,0,1,0] => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => 1
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[4,2] => [1,1,1,0,0,1,0,0,1,0] => 3
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,2,1] => [1,0,1,0,1,0,1,0] => 4
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[4,3] => [1,1,1,0,0,0,1,0,1,0] => 3
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 3
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 4
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 1
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 4
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
>>> Load all 131 entries. <<<
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 4
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 4
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 4
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 5
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 5
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
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Description
The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.