Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
St001236: Integer compositions ⟶ ℤ
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] => 1
[1,1,0,0,1,0] => [2,1] => 1
[1,1,0,1,0,0] => [2,1] => 1
[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] => 1
[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] => 1
[1,1,0,0,1,0,1,0] => [2,1,1] => 1
[1,1,0,0,1,1,0,0] => [2,2] => 1
[1,1,0,1,0,0,1,0] => [2,1,1] => 1
[1,1,0,1,0,1,0,0] => [2,1,1] => 1
[1,1,0,1,1,0,0,0] => [2,2] => 1
[1,1,1,0,0,0,1,0] => [3,1] => 1
[1,1,1,0,0,1,0,0] => [3,1] => 1
[1,1,1,0,1,0,0,0] => [3,1] => 1
[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] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,2,2] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,4] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,3] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,2,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,2,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,2,1] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,3] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2] => 1
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,2] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,1] => 1
[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] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 1
[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] => 1
[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] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 1
[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] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => 1
[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] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => 1
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Description
The dominant dimension of the corresponding Comp-Nakayama algebra.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
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