Identifier
- St001253: 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]=>1
[1,0,1,1,0,0]=>0
[1,1,0,0,1,0]=>0
[1,1,0,1,0,0]=>0
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0]=>0
[1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0]=>0
[1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0]=>0
[1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0]=>0
[1,1,1,0,0,0,1,0]=>0
[1,1,1,0,0,1,0,0]=>0
[1,1,1,0,1,0,0,0]=>0
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>0
[1,0,1,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0]=>0
[1,0,1,1,1,0,0,1,0,0]=>0
[1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0]=>0
[1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>0
[1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0]=>0
[1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0]=>0
[1,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0]=>0
[1,1,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>0
[1,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0]=>0
[1,1,1,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>0
[1,1,1,1,0,0,1,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,0]=>3
[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]=>3
[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0]=>3
[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]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0]=>1
[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]=>1
[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]=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>0
[1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[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]=>4
[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>0
[1,0,1,1,1,0,0,1,0,0,1,0]=>1
[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]=>0
[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>0
[1,0,1,1,1,1,0,0,0,1,0,0]=>0
[1,0,1,1,1,1,0,0,1,0,0,0]=>0
[1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0]=>0
[1,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0]=>0
[1,1,0,0,1,1,1,0,0,1,0,0]=>0
[1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>1
[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]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,0]=>3
[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]=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>0
[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[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]=>3
[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>0
[1,1,0,1,1,1,0,0,0,1,0,0]=>0
[1,1,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,0]=>0
[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>0
[1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>0
[1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>0
[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,0]=>0
[1,1,1,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,0]=>0
[1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>0
[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>0
[1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,0,1,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>0
[1,1,1,1,1,0,0,0,1,0,0,0]=>0
[1,1,1,1,1,0,0,1,0,0,0,0]=>0
[1,1,1,1,1,0,1,0,0,0,0,0]=>0
[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]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>4
[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]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4
[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]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>3
[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]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[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]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[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]=>1
[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]=>2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[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]=>2
[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]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1
[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]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[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]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>0
[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]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[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]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>5
[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]=>4
[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]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[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]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[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]=>4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[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]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[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]=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>2
[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]=>1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[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]=>3
[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]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3
[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]=>2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2
[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]=>4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
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Description
The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra.
For the first 196 values the statistic coincides also with the number of fixed points of $\tau \Omega^2$ composed with its inverse, see theorem 5.8. in the reference for more details.
The number of Dyck paths of length n where the statistics returns zero seems to be 2^(n-1).
For the first 196 values the statistic coincides also with the number of fixed points of $\tau \Omega^2$ composed with its inverse, see theorem 5.8. in the reference for more details.
The number of Dyck paths of length n where the statistics returns zero seems to be 2^(n-1).
References
[1] Iyama, O., Solberg, Øyvind Auslander-Gorenstein algebras and precluster tilting. zbMATH:06833443
Code
DeclareOperation("IsNthSyzygy",[IsList]);
InstallMethod(IsNthSyzygy, "for a representation of a quiver", [IsList],0,function(LIST)
local M,n,N,W;
M:=LIST[1];
n:=LIST[2];
N:=DualOfModule(NthSyzygy(DualOfModule(M),n));
W:=NthSyzygy(N,n);
if IsDirectSummand(M,W)=true
then
return(1);
else return(0);
fi;
end);
DeclareOperation("NumberOfReflexiveModules",[IsList]);
InstallMethod(NumberOfReflexiveModules, "for a representation of a quiver", [IsList],0,function(LIST)
local L,A,LL1,LL2;
L:=LIST[1];
A:=NakayamaAlgebra(L,GF(3));
L:=ARQuiverNak([A]);L:=Filtered(L,x->IsProjectiveModule(x)=false);
LL1:=Filtered(L,x->DominantDimensionOfModule(x,30)>=1);
LL2:=Filtered(LL1,x->IsNthSyzygy([x,2])=1);
return(Size(LL2));
end);
Created
Sep 08, 2018 at 11:49 by Rene Marczinzik
Updated
Oct 20, 2018 at 20:19 by Rene Marczinzik
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