Identifier
Identifier
  • St001068: Dyck paths ⟶ ℤ (values match St000015The number of peaks of a Dyck path., St000053The number of valleys of the Dyck path., St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra.)
Values
[1,0] generating graphics... => 1
[1,0,1,0] generating graphics... => 2
[1,1,0,0] generating graphics... => 1
[1,0,1,0,1,0] generating graphics... => 3
[1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] generating graphics... => 1
click to show generating function       
Description
Number of torsionless simple modules in the corresponding Nakayama algebra.
Code
DeclareOperation("IsNthSyzygy",[IsList]);

InstallMethod(IsNthSyzygy, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h,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("NumberOfTorsionlessSimpleModules",[IsList]);

InstallMethod(NumberOfTorsionlessSimpleModules, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h,W;

L:=LIST[1];

A:=NakayamaAlgebra(L,GF(3));
simA:=SimpleModules(A);
U:=Filtered(simA,x->IsNthSyzygy([x,1])=1);
return(Size(U));


end);


Created
Dec 30, 2017 at 14:43 by Rene Marczinzik
Updated
Dec 30, 2017 at 14:43 by Rene Marczinzik