Identifier
-
Mp00231:
Integer compositions
—bounce path⟶
Dyck paths
St001200: Dyck paths ⟶ ℤ
Values
[1,1] => [1,0,1,0] => 2
[1,1,1] => [1,0,1,0,1,0] => 3
[1,2] => [1,0,1,1,0,0] => 2
[2,1] => [1,1,0,0,1,0] => 2
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 3
[1,1,2] => [1,0,1,0,1,1,0,0] => 3
[1,2,1] => [1,0,1,1,0,0,1,0] => 3
[1,3] => [1,0,1,1,1,0,0,0] => 2
[2,1,1] => [1,1,0,0,1,0,1,0] => 3
[2,2] => [1,1,0,0,1,1,0,0] => 2
[3,1] => [1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 3
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 3
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 3
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
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Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
bounce path
Description
The bounce path determined by an integer composition.
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