Identifier
- St000688: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>0
[1,0,1,0]=>0
[1,1,0,0]=>0
[1,0,1,0,1,0]=>0
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>1
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0]=>0
[1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0]=>0
[1,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>0
[1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>0
[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0]=>1
[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]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2
[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]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
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Description
The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path.
The global dimension is given by St000684The global dimension of the LNakayama algebra associated to a Dyck path. and the dominant dimension is given by St000685The dominant dimension of the LNakayama algebra associated to a Dyck path.. To every Dyck path there is an LNakayama algebra associated as described in St000684The global dimension of the LNakayama algebra associated to a Dyck path..
Dyck paths for which the global dimension and the dominant dimension of the the LNakayama algebra coincide and both dimensions at least $2$ correspond to the LNakayama algebras that are higher Auslander algebras in the sense of [1].
The global dimension is given by St000684The global dimension of the LNakayama algebra associated to a Dyck path. and the dominant dimension is given by St000685The dominant dimension of the LNakayama algebra associated to a Dyck path.. To every Dyck path there is an LNakayama algebra associated as described in St000684The global dimension of the LNakayama algebra associated to a Dyck path..
Dyck paths for which the global dimension and the dominant dimension of the the LNakayama algebra coincide and both dimensions at least $2$ correspond to the LNakayama algebras that are higher Auslander algebras in the sense of [1].
References
[1] Iyama, O. Auslander correspondence MathSciNet:2298820
Code
BuildSequencesLNak:=function(n)
local all,range,len,new,seq,i,sel;
all:=[[1]];
range:=[2..n];
for len in [1..n-1] do
new:=[];
for seq in all do
sel:=Filtered(range, x->x<=1+seq[1]);
for i in sel do
Add(new,Concatenation([i],seq));
od;
od;
all:=new;
od;
return all;
end;
DeclareOperation("ProjToInjNak", [IsList]);
InstallMethod(ProjToInjNak, "for a representation of a quiver", [IsList],0,function(L)
local list, n, temp1, Liste_d, j, i, k, r, kk;
list:=L;
n:=Size(L);
temp1:=[];
Liste_d:=[];
for j in [1..n] do
for k in L do
r:=(j-k) mod n;
if r=0 then r:=n; fi;
if k>=L[r] then
Append(temp1,[k]);
fi;
od;
kk:=Minimum(temp1);
temp1:=[];
Append(Liste_d,[kk]);
od;
return(Liste_d);
end
);
DeclareOperation("domdimlist", [IsList]);
InstallMethod(domdimlist, "for a representation of a quiver", [IsList],0,function(L)
local list, n, Liste_d, i, Expr1, Expr2, Expr3, r, s, List1, List2, List_not_in_List2, m, f, g, x, y, j, List_for_dom, temp2, dd, z;
list:=L;
n:=Size(L);
Liste_d:=ProjToInjNak(L);
List1:=[];
List2:=[];
for i in [1..n] do
r:=i mod n; if r =0 then r:=n; fi;
s:=(i+1) mod n; if s = 0 then s:=n; fi;
if Liste_d[s]<=Liste_d[r] then
Append(List1,[i-1]);
fi;
od;
for i in [1..n] do
r:=i mod n; if r =0 then r:=n; fi;
s:=(i-1) mod n; if s = 0 then s:=n; fi;
if L[s]<=L[r] then
Append(List2,[i-1]);
fi;
od;
List_not_in_List2:=[];
for i in [0..n-1] do
if (i in List2)=false then
Append(List_not_in_List2,[i]);
fi;
od;
List_for_dom:=[];
m:=Size(List_not_in_List2);
for j in List_not_in_List2 do
Append(List_for_dom,[[[j+L[j+1]-1,L[j+1]]]]);
od;
f := function (x,y)
local c;
c:=(x-y) mod n; if c=0 then c:=n; fi;
z:=(x+1) mod n; if z=0 then z:=n; fi;
return([c,Liste_d[z]-y]);
end;
for r in [1..m] do
s:=Size(List_for_dom[r]);
while (f(List_for_dom[r][s][1],List_for_dom[r][s][2])[1] mod n in List1) = true do
Append(List_for_dom[r],[f(List_for_dom[r][s][1],List_for_dom[r][s][2])]);
s:=Size(List_for_dom[r]);
od;
s:=0;
od;
temp2:=[];
for i in [1..Size(List_for_dom)] do
Append(temp2,[Size(List_for_dom[i])]);
od;
dd:=Minimum(temp2);
return(dd);
end
);
DeclareOperation("gldim", [IsList]);
InstallMethod(gldim, "for a representation of a quiver", [IsList],0,function(L)
local list, n, i, j, f, temp, temp2, temp3, u;
list:=L;
n:=Size(L);
f := function (x,y)
local c, z;
c:=(x+y) mod n; if c=0 then c:=n; fi;
z:=(x+1) mod n; if z=0 then z:=n; fi;
return([c,list[z]-y]);
end;
temp2:=[];
for i in [0..n-1] do
Append(temp2,[[i,1]]);
od;
temp:=[];
for i in [0..n-1] do
u:=temp2[i+1];
Append(temp,[[u]]);
od;
for i in [0..n-1] do
j:=1;
while j<(2*n+3) do
Append(temp[i+1],[f(temp[i+1][j][1],temp[i+1][j][2])]);
j:=j+1;
od;
od;
temp3:=[];
for i in [1..n] do
temp2:=[];
for j in [1..(2*n+3)] do
if temp[i][j][2]=0 then Append(temp2,[j]); fi;
od;
if Size(temp2)>0 then
u:=Minimum(temp2);
Append(temp3,[u]);
else
temp3:="inf"; break;
fi;
od;
if IsString(temp3)=false then
temp3:=(Maximum(temp3))-2;
fi;
return(temp3);
end
);
Created
Jan 12, 2017 at 14:05 by Rene Marczinzik
Updated
Jan 12, 2017 at 15:19 by Christian Stump
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