Identifier
-
Mp00043:
Integer partitions
—to Dyck path⟶
Dyck paths
St001064: Dyck paths ⟶ ℤ
Values
=>
Cc0002;cc-rep-0
Cc0005;cc-rep
[1]=>[1,0,1,0]=>1
[2]=>[1,1,0,0,1,0]=>1
[1,1]=>[1,0,1,1,0,0]=>1
[3]=>[1,1,1,0,0,0,1,0]=>1
[2,1]=>[1,0,1,0,1,0]=>1
[1,1,1]=>[1,0,1,1,1,0,0,0]=>1
[4]=>[1,1,1,1,0,0,0,0,1,0]=>1
[3,1]=>[1,1,0,1,0,0,1,0]=>1
[2,2]=>[1,1,0,0,1,1,0,0]=>1
[2,1,1]=>[1,0,1,1,0,1,0,0]=>1
[1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0]=>1
[5]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[4,1]=>[1,1,1,0,1,0,0,0,1,0]=>1
[3,2]=>[1,1,0,0,1,0,1,0]=>1
[3,1,1]=>[1,0,1,1,0,0,1,0]=>1
[2,2,1]=>[1,0,1,0,1,1,0,0]=>1
[2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0]=>1
[1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>1
[5,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[4,2]=>[1,1,1,0,0,1,0,0,1,0]=>1
[4,1,1]=>[1,1,0,1,1,0,0,0,1,0]=>1
[3,3]=>[1,1,1,0,0,0,1,1,0,0]=>1
[3,2,1]=>[1,0,1,0,1,0,1,0]=>2
[3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0]=>1
[2,2,2]=>[1,1,0,0,1,1,1,0,0,0]=>1
[2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0]=>1
[2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[6,1]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>1
[5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>1
[5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>1
[4,3]=>[1,1,1,0,0,0,1,0,1,0]=>1
[4,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>2
[4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0]=>1
[3,3,1]=>[1,1,0,1,0,0,1,1,0,0]=>1
[3,2,2]=>[1,1,0,0,1,1,0,1,0,0]=>1
[3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0]=>2
[3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>1
[2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0]=>1
[2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>1
[2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1
[6,2]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1
[6,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1
[5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>1
[4,4]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>1
[4,3,1]=>[1,1,0,1,0,0,1,0,1,0]=>1
[4,2,2]=>[1,1,0,0,1,1,0,0,1,0]=>1
[4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0]=>2
[4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[3,3,2]=>[1,1,0,0,1,0,1,1,0,0]=>1
[3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0]=>1
[3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0]=>2
[3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1
[2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>1
[2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>1
[2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1
[6,3]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1
[6,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>2
[6,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1
[5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>1
[5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>1
[5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>1
[4,3,2]=>[1,1,0,0,1,0,1,0,1,0]=>2
[4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>1
[4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>1
[4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1
[3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>1
[3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0]=>2
[3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>1
[3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>2
[2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>1
[2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1
[6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1
[6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1
[6,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>1
[6,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2
[6,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>1
[5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1
[5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>1
[5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>1
[5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>1
[5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1
[4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>1
[4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>1
[4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>1
[4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>3
[4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>1
[4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>1
[4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>2
[3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>1
[3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>1
[3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>1
[3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2
[2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>1
[2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>1
[6,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1
[6,4,1]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>1
[6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2
[6,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>1
[6,2,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>1
[6,2,1,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>2
[6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1
[5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>1
[5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>1
[5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>1
[5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>2
[5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>1
[5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>1
[5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>1
[5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2
[4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>1
[4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>1
[4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>1
[4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>2
[4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>1
[4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>1
[4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2
[3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>1
[3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>1
[3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2
[3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>1
[3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2
[2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>1
[6,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>1
[6,4,2]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>1
[6,4,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>1
[6,3,3]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>1
[6,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[6,3,1,1,1]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>1
[6,2,2,2]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>1
[6,2,2,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>1
[6,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2
[5,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>1
[5,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>1
[5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>2
[5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>1
[5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>3
[5,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>1
[5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[5,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>2
[4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>1
[4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>1
[4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>1
[4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>1
[4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>1
[4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>3
[4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>1
[4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>2
[3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>1
[3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>1
[3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>1
[3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>2
[3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>2
[6,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>1
[6,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>1
[6,4,3]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>2
[6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>1
[6,4,1,1,1]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>1
[6,3,3,1]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>1
[6,3,2,2]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>2
[6,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[6,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>1
[6,2,2,2,1]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>1
[6,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>1
[5,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>1
[5,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>2
[5,5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,4,4]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>1
[5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>2
[5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>2
[5,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>1
[5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>1
[5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>1
[5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>3
[5,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[5,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>1
[5,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>1
[4,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>1
[4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>1
[4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>1
[4,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>2
[4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>1
[4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>3
[4,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>1
[4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>2
[4,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>1
[3,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>1
[3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>1
[3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>2
[3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>2
[6,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>1
[6,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[6,5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>1
[6,4,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>1
[6,4,3,1]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,4,2,2]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>1
[6,4,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[6,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>1
[6,3,3,2]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>1
[6,3,3,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>1
[6,3,2,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[6,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>3
[6,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>1
[6,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>1
[5,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>1
[5,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>1
[5,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>1
[5,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>2
[5,5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>1
[5,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>1
[5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>3
[5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>2
[5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>1
[5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>2
[5,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>1
[5,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>2
[5,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>3
[5,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>1
[4,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>1
[4,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>1
[4,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>1
[4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>3
[4,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>1
[4,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>1
[4,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>2
[4,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>1
[4,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>2
[4,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>3
[3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>1
[3,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1
[3,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>2
[6,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>2
[6,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>1
[6,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>1
[6,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[6,5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>1
[6,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>1
[6,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[6,4,3,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,4,2,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[6,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[6,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>1
[6,3,3,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>1
[6,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>1
[6,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>2
[6,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>3
[6,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1
[5,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>1
[5,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[5,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>1
[5,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>1
[5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>2
[5,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>1
[5,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>1
[5,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>2
[5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>4
[5,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>1
[5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>1
[5,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>1
[5,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>2
[5,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>3
[5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>3
[4,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>1
[4,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>2
[4,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1
[4,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>1
[4,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>2
[4,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[4,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1
[4,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>2
[4,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1
[4,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>3
[3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>2
[6,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[6,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>1
[6,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>1
[6,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[6,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>1
[6,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>1
[6,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>2
[6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>3
[6,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>1
[6,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[6,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>1
[6,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1
[6,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[6,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>3
[5,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>1
[5,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>1
[5,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>1
[5,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[5,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1
[5,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>1
[5,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1
[5,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>2
[5,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1
[5,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>3
[5,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1
[5,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1
[5,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1
[5,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>3
[4,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1
[4,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1
[4,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>2
[4,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>2
[4,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1
[4,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>3
[4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>3
[6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[6,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>1
[6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>2
[6,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1
[6,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1
[6,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1
[6,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>1
[6,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[6,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1
[6,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[6,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>3
[6,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1
[6,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1
[6,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1
[6,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[5,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>2
[5,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1
[5,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1
[5,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>2
[5,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>3
[5,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1
[5,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[5,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1
[5,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>3
[5,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>3
[5,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>2
[4,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>1
[4,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>1
[4,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>3
[6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>5
[5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>4
[6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>3
[5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>4
[4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3
[6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[5,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[6,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>4
[5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[6,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>1
[6,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1
[5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>1
[6,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3
[5,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>3
[6,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[6,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>1
[6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3
[5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1
[5,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1
[5,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>1
[6,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3
[5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[6,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[6,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3
[6,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>4
[5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>3
[6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>3
[6,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1
[5,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1
[6,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>3
[6,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[5,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1
[6,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1
[6,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1
[6,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[6,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>3
[6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>3
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Description
Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules.
Map
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Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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