Identifier
-
Mp00230:
Integer partitions
—parallelogram polyomino⟶
Dyck paths
St001034: Dyck paths ⟶ ℤ
Values
=>
Cc0002;cc-rep-0
Cc0005;cc-rep
[1]=>[1,0]=>1
[2]=>[1,0,1,0]=>2
[1,1]=>[1,1,0,0]=>2
[3]=>[1,0,1,0,1,0]=>3
[2,1]=>[1,0,1,1,0,0]=>3
[1,1,1]=>[1,1,0,1,0,0]=>3
[4]=>[1,0,1,0,1,0,1,0]=>4
[3,1]=>[1,0,1,0,1,1,0,0]=>4
[2,2]=>[1,1,1,0,0,0]=>4
[2,1,1]=>[1,0,1,1,0,1,0,0]=>4
[1,1,1,1]=>[1,1,0,1,0,1,0,0]=>4
[5]=>[1,0,1,0,1,0,1,0,1,0]=>5
[4,1]=>[1,0,1,0,1,0,1,1,0,0]=>5
[3,2]=>[1,0,1,1,1,0,0,0]=>5
[3,1,1]=>[1,0,1,0,1,1,0,1,0,0]=>5
[2,2,1]=>[1,1,1,0,0,1,0,0]=>5
[2,1,1,1]=>[1,0,1,1,0,1,0,1,0,0]=>5
[1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>5
[6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>6
[4,2]=>[1,0,1,0,1,1,1,0,0,0]=>6
[4,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>6
[3,3]=>[1,1,1,0,1,0,0,0]=>6
[3,2,1]=>[1,0,1,1,1,0,0,1,0,0]=>6
[3,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>6
[2,2,2]=>[1,1,1,1,0,0,0,0]=>6
[2,2,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>6
[2,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>6
[1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>6
[7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>7
[6,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>7
[5,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>7
[5,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>7
[4,3]=>[1,0,1,1,1,0,1,0,0,0]=>7
[4,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>7
[4,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>7
[3,3,1]=>[1,1,1,0,1,0,0,1,0,0]=>7
[3,2,2]=>[1,0,1,1,1,1,0,0,0,0]=>7
[3,2,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>7
[3,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>7
[2,2,2,1]=>[1,1,1,1,0,0,0,1,0,0]=>7
[2,2,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>7
[2,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>8
[7,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>8
[6,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>8
[6,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8
[5,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>8
[5,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>8
[5,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>8
[4,4]=>[1,1,1,0,1,0,1,0,0,0]=>8
[4,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>8
[4,2,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>8
[4,2,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>8
[4,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>8
[3,3,2]=>[1,1,1,0,1,1,0,0,0,0]=>8
[3,3,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>8
[3,2,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>8
[3,2,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>8
[3,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>8
[2,2,2,2]=>[1,1,1,1,0,1,0,0,0,0]=>8
[2,2,2,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>8
[2,2,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>8
[2,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>8
[9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>9
[8,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>9
[7,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>9
[7,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>9
[6,3]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>9
[6,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>9
[6,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>9
[5,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>9
[5,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>9
[5,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>9
[5,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>9
[5,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>9
[4,4,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>9
[4,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>9
[4,3,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>9
[4,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>9
[4,2,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>9
[4,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>9
[3,3,3]=>[1,1,1,1,1,0,0,0,0,0]=>9
[3,3,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>9
[3,3,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>9
[3,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>9
[3,2,2,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>9
[3,2,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>9
[3,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[2,2,2,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>9
[2,2,2,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>9
[2,2,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[2,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>9
[10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>10
[9,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>10
[8,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>10
[8,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>10
[7,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>10
[7,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>10
[7,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>10
[6,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>10
[6,3,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>10
[6,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>10
[6,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>10
[6,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>10
[5,5]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>10
[5,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>10
[5,3,2]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>10
[5,3,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>10
[5,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>10
[5,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>10
[5,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>10
[4,4,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>10
[4,4,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>10
[4,3,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>10
[4,3,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>10
[4,3,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>10
[4,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>10
[4,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>10
[4,2,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>10
[4,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>10
[3,3,3,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>10
[3,3,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>10
[3,3,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>10
[3,3,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>10
[3,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>10
[3,2,2,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>10
[3,2,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>10
[3,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>10
[2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>10
[2,2,2,2,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>10
[2,2,2,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>10
[2,2,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>10
[2,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>10
[1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>10
[10,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>11
[9,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>11
[7,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>11
[6,5]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>11
[6,4,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>11
[6,3,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>11
[5,5,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>11
[5,4,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>11
[5,4,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>11
[5,3,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>11
[5,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>11
[5,3,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>11
[5,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>11
[5,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>11
[4,4,3]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>11
[4,4,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>11
[4,4,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>11
[4,3,3,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>11
[4,3,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>11
[4,3,2,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>11
[4,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>11
[3,3,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>11
[3,3,3,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>11
[3,3,2,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>11
[3,3,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>11
[3,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>11
[3,2,2,2,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>11
[2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>11
[2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>11
[2,2,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>11
[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>11
[7,5]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>12
[6,6]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>12
[6,5,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>12
[6,4,2]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>12
[6,4,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>12
[6,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>12
[5,5,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>12
[5,4,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>12
[5,4,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>12
[5,4,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>12
[5,3,3,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>12
[5,3,2,2]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>12
[5,3,2,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>12
[5,2,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>12
[4,4,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>12
[4,4,3,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>12
[4,4,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>12
[4,4,2,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>12
[4,3,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>12
[4,3,3,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>12
[4,3,2,2,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>12
[4,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>12
[3,3,3,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>12
[3,3,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>12
[3,3,3,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>12
[3,3,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>12
[3,3,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>12
[3,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>12
[2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>12
[2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>12
[7,6]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>13
[6,6,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>13
[6,5,2]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>13
[6,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>13
[5,5,3]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>13
[5,4,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>13
[5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>13
[5,4,2,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>13
[5,4,2,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>13
[5,3,3,2]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>13
[5,3,3,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>13
[5,3,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>13
[4,4,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>13
[4,4,3,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>13
[4,4,3,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>13
[4,4,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>13
[4,3,3,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>13
[4,3,3,2,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>13
[4,3,2,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>13
[3,3,3,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>13
[3,3,3,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>13
[3,3,2,2,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>13
[3,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>13
[2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>13
[7,7]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>14
[7,6,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>14
[6,6,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>14
[6,5,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>14
[6,4,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>14
[5,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>14
[5,5,2,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>14
[5,5,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>14
[5,4,4,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>14
[5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>14
[5,4,3,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>14
[5,4,2,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>14
[5,3,3,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>14
[5,3,3,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>14
[4,4,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>14
[4,4,3,3]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>14
[4,4,3,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>14
[4,4,2,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>14
[4,3,3,3,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>14
[4,3,3,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>14
[3,3,3,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>14
[3,3,3,3,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>14
[3,3,2,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>14
[2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>14
[8,7]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>15
[7,7,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>15
[6,6,3]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>15
[6,5,4]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>15
[5,5,5]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>15
[5,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>15
[5,5,3,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>15
[5,4,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>15
[5,4,3,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>15
[5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>15
[4,4,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>15
[4,4,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>15
[4,4,3,3,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>15
[4,4,3,2,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>15
[4,3,3,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>15
[3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>15
[3,3,3,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>15
[3,3,3,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>15
[3,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>15
[8,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>16
[6,6,4]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>16
[6,5,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>16
[5,5,5,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>16
[5,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>16
[5,5,3,3]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>16
[5,4,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>16
[4,4,4,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>16
[4,4,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>16
[4,4,4,2,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>16
[4,4,3,3,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>16
[4,3,3,3,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>16
[4,3,3,2,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>16
[3,3,3,3,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>16
[3,3,3,3,2,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>16
[2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>16
[9,8]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>17
[8,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>17
[6,6,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>17
[5,5,5,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>17
[5,5,4,3]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>17
[5,4,4,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>17
[4,4,4,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>17
[4,4,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>17
[4,4,3,3,3]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>17
[3,3,3,3,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>17
[3,3,3,2,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>17
[3,2,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>17
[]=>[]=>0
[6,5,4,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>18
[6,5,4,3,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>24
[4,4,4,4,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>20
[5,4,4,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>20
[4,4,4,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>18
[2,2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>18
[3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>18
[3,3,3,3,3,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>19
[4,3,3,3,3,3]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>19
[4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>20
[4,4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>24
[5,5,5,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>20
[6,6,6,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>24
[6,6,6]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>18
[7,6,6]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>19
[10,10]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>20
[6,6,6,6,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>30
[5,5,5,5,5,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>30
[5,5,5,5,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>25
[9,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>18
[6,5,5,5]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>21
[5,4,4,4,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>21
[4,4,4,4,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>21
[5,5,5,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>21
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Description
The area of the parallelogram polyomino associated with the Dyck path.
The (bivariate) generating function is given in [1].
The (bivariate) generating function is given in [1].
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
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