Identifier
- St001994: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>2
[1,0,1,0]=>3
[1,1,0,0]=>3
[1,0,1,0,1,0]=>4
[1,0,1,1,0,0]=>4
[1,1,0,0,1,0]=>4
[1,1,0,1,0,0]=>4
[1,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,0]=>5
[1,1,1,0,0,0,1,0]=>5
[1,1,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,0,0]=>5
[1,1,1,1,0,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,1,1,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,0]=>6
[1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0]=>5
[1,0,1,1,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,1,0,0]=>6
[1,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,1,1,0,0,0]=>6
[1,1,0,1,0,0,1,0,1,0]=>6
[1,1,0,1,0,0,1,1,0,0]=>6
[1,1,0,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,0]=>6
[1,1,0,1,0,1,1,0,0,0]=>6
[1,1,0,1,1,0,0,0,1,0]=>6
[1,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,0,0,0]=>5
[1,1,0,1,1,1,0,0,0,0]=>6
[1,1,1,0,0,0,1,0,1,0]=>6
[1,1,1,0,0,0,1,1,0,0]=>6
[1,1,1,0,0,1,0,0,1,0]=>6
[1,1,1,0,0,1,0,1,0,0]=>6
[1,1,1,0,0,1,1,0,0,0]=>6
[1,1,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,0,0,1,0,0]=>6
[1,1,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,0,0,0]=>6
[1,1,1,1,0,0,0,0,1,0]=>6
[1,1,1,1,0,0,0,1,0,0]=>6
[1,1,1,1,0,0,1,0,0,0]=>6
[1,1,1,1,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,0,1,1,0,0]=>7
[1,0,1,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,0,1,0,1,1,1,0,0,0]=>7
[1,0,1,0,1,1,0,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,0,1,1,0,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,1,0,1,1,0,0,0]=>6
[1,0,1,0,1,1,1,0,0,0,1,0]=>7
[1,0,1,0,1,1,1,0,0,1,0,0]=>7
[1,0,1,0,1,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,1,1,0,0,0,0]=>7
[1,0,1,1,0,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,0,1,0,1,1,0,0]=>7
[1,0,1,1,0,0,1,1,0,0,1,0]=>7
[1,0,1,1,0,0,1,1,0,1,0,0]=>6
[1,0,1,1,0,0,1,1,1,0,0,0]=>7
[1,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,1,0,0,0]=>6
[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[1,0,1,1,0,1,1,0,0,1,0,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,0]=>5
[1,0,1,1,0,1,1,1,0,0,0,0]=>6
[1,0,1,1,1,0,0,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,0,1,1,0,0]=>7
[1,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,0,1,1,1,0,0,1,0,1,0,0]=>7
[1,0,1,1,1,0,0,1,1,0,0,0]=>7
[1,0,1,1,1,0,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,0,0]=>6
[1,0,1,1,1,1,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,0,0,0,1,0,0]=>7
[1,0,1,1,1,1,0,0,1,0,0,0]=>7
[1,0,1,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0]=>7
[1,1,0,0,1,0,1,0,1,1,0,0]=>7
[1,1,0,0,1,0,1,1,0,0,1,0]=>7
[1,1,0,0,1,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,0,1,1,1,0,0,0]=>7
[1,1,0,0,1,1,0,0,1,0,1,0]=>7
[1,1,0,0,1,1,0,0,1,1,0,0]=>7
[1,1,0,0,1,1,0,1,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,1,0,0]=>6
[1,1,0,0,1,1,0,1,1,0,0,0]=>6
[1,1,0,0,1,1,1,0,0,0,1,0]=>7
[1,1,0,0,1,1,1,0,0,1,0,0]=>7
[1,1,0,0,1,1,1,0,1,0,0,0]=>6
[1,1,0,0,1,1,1,1,0,0,0,0]=>7
[1,1,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,0,1,0,0,1,0,1,1,0,0]=>7
[1,1,0,1,0,0,1,1,0,0,1,0]=>7
[1,1,0,1,0,0,1,1,0,1,0,0]=>6
[1,1,0,1,0,0,1,1,1,0,0,0]=>7
[1,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,1,0,1,0,1,0,0,1,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,0,1,0]=>7
[1,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,1,0,0,0]=>7
[1,1,0,1,0,1,1,0,0,0,1,0]=>7
[1,1,0,1,0,1,1,0,0,1,0,0]=>6
[1,1,0,1,0,1,1,0,1,0,0,0]=>6
[1,1,0,1,0,1,1,1,0,0,0,0]=>7
[1,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,0,1,1,0,0]=>7
[1,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,1,0,0]=>6
[1,1,0,1,1,0,0,1,1,0,0,0]=>6
[1,1,0,1,1,0,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,1,0,0,1,0,0]=>6
[1,1,0,1,1,0,1,0,1,0,0,0]=>6
[1,1,0,1,1,0,1,1,0,0,0,0]=>6
[1,1,0,1,1,1,0,0,0,0,1,0]=>7
[1,1,0,1,1,1,0,0,0,1,0,0]=>7
[1,1,0,1,1,1,0,0,1,0,0,0]=>6
[1,1,0,1,1,1,0,1,0,0,0,0]=>6
[1,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,1,1,0,0,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,0,1,0,1,1,0,0]=>7
[1,1,1,0,0,0,1,1,0,0,1,0]=>7
[1,1,1,0,0,0,1,1,0,1,0,0]=>6
[1,1,1,0,0,0,1,1,1,0,0,0]=>7
[1,1,1,0,0,1,0,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,0,1,1,0,0]=>7
[1,1,1,0,0,1,0,1,0,0,1,0]=>7
[1,1,1,0,0,1,0,1,0,1,0,0]=>7
[1,1,1,0,0,1,0,1,1,0,0,0]=>7
[1,1,1,0,0,1,1,0,0,0,1,0]=>7
[1,1,1,0,0,1,1,0,0,1,0,0]=>6
[1,1,1,0,0,1,1,0,1,0,0,0]=>6
[1,1,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,1,0,1,0,0,0,1,0,1,0]=>7
[1,1,1,0,1,0,0,0,1,1,0,0]=>7
[1,1,1,0,1,0,0,1,0,0,1,0]=>7
[1,1,1,0,1,0,0,1,0,1,0,0]=>7
[1,1,1,0,1,0,0,1,1,0,0,0]=>7
[1,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,1,1,0,1,0,1,0,0,1,0,0]=>7
[1,1,1,0,1,0,1,0,1,0,0,0]=>7
[1,1,1,0,1,0,1,1,0,0,0,0]=>7
[1,1,1,0,1,1,0,0,0,0,1,0]=>7
[1,1,1,0,1,1,0,0,0,1,0,0]=>6
[1,1,1,0,1,1,0,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,1,0,0,0,0]=>6
[1,1,1,0,1,1,1,0,0,0,0,0]=>7
[1,1,1,1,0,0,0,0,1,0,1,0]=>7
[1,1,1,1,0,0,0,0,1,1,0,0]=>7
[1,1,1,1,0,0,0,1,0,0,1,0]=>7
[1,1,1,1,0,0,0,1,0,1,0,0]=>7
[1,1,1,1,0,0,0,1,1,0,0,0]=>7
[1,1,1,1,0,0,1,0,0,0,1,0]=>7
[1,1,1,1,0,0,1,0,0,1,0,0]=>7
[1,1,1,1,0,0,1,0,1,0,0,0]=>7
[1,1,1,1,0,0,1,1,0,0,0,0]=>7
[1,1,1,1,0,1,0,0,0,0,1,0]=>7
[1,1,1,1,0,1,0,0,0,1,0,0]=>7
[1,1,1,1,0,1,0,0,1,0,0,0]=>7
[1,1,1,1,0,1,0,1,0,0,0,0]=>7
[1,1,1,1,0,1,1,0,0,0,0,0]=>7
[1,1,1,1,1,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,0,0,0,0,1,0,0]=>7
[1,1,1,1,1,0,0,0,1,0,0,0]=>7
[1,1,1,1,1,0,0,1,0,0,0,0]=>7
[1,1,1,1,1,0,1,0,0,0,0,0]=>7
[1,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>7
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>8
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>6
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>7
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>8
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>7
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>8
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>8
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>7
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>6
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>7
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>7
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>7
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>7
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>7
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>8
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>7
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>8
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>8
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>8
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>8
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>8
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>7
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>8
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>8
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>6
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>8
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>7
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>7
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>7
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>6
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>7
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>7
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>8
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>8
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>7
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>8
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>8
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>8
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>8
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>8
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>7
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>7
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>6
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>7
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>7
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>6
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>6
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>6
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>6
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>8
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>7
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>8
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>6
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>7
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>8
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>8
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>8
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>7
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>8
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>8
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>8
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>7
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>6
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>8
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>8
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>7
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>8
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>8
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>8
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>8
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>7
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>8
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>8
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>7
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>6
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>8
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>8
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>7
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>8
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>8
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>7
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>8
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>8
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>8
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>8
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>7
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>8
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>8
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>8
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>8
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>8
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>8
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>8
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>8
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>8
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>8
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>8
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>8
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>8
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>8
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>8
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>8
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>8
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>8
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>8
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Description
The number of simple spherical modules of the corresponding linear Nakayama algebra.
A module $M$ with projective dimension $n$ is spherical (in the sense of Auslander and Bridger) if $Ext_A^i(M,A) =0$ for $i=1,\dots,n-1$. By convention all modules of projective dimension at most 1 are spherical.
A module $M$ with projective dimension $n$ is spherical (in the sense of Auslander and Bridger) if $Ext_A^i(M,A) =0$ for $i=1,\dots,n-1$. By convention all modules of projective dimension at most 1 are spherical.
References
[1] Auslander, M., Bridger, M. Stable module theory MathSciNet:0269685
Code
DeclareOperation("issphericalmodule",[IsList]);
InstallMethod(issphericalmodule, "for a representation of a quiver", [IsList],0,function(LIST)
local A,M,n,RegA,W,i,WW;
A:=LIST[1];
M:=LIST[2];
n:=ProjDimensionOfModule(M,33);
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
if n<=1 then return(1=1);else
W:=[];for i in [0..n-2] do Append(W,[Size(ExtOverAlgebra(NthSyzygy(M,i),RegA)[2])]);od;
WW:=Filtered(W,x->(x=0));
return(Size(W)=Size(WW));fi;
end);
DeclareOperation("numberofsphericalsimplemodules",[IsList]);
InstallMethod(numberofsphericalsimplemodules, "for a representation of a quiver", [IsList],0,function(LIST)
local A,L,LL,B,C;
A:=LIST[1];
L:=SimpleModules(A);
LL:=Filtered(L,x->issphericalmodule([A,x])=true);
return(Size(LL));
end);
Created
May 12, 2026 at 14:20 by Rene Marczinzik
Updated
May 12, 2026 at 14:43 by Martin Rubey
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