Identifier
-
Mp00037:
Graphs
—to partition of connected components⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001541: Integer partitions ⟶ ℤ
Values
=>
Cc0020;cc-rep-0
Cc0002;cc-rep-1
Cc0002;cc-rep
([],2)=>[1,1]=>[1]=>0
([],3)=>[1,1,1]=>[1,1]=>0
([(1,2)],3)=>[2,1]=>[1]=>0
([],4)=>[1,1,1,1]=>[1,1,1]=>0
([(2,3)],4)=>[2,1,1]=>[1,1]=>0
([(1,3),(2,3)],4)=>[3,1]=>[1]=>0
([(0,3),(1,2)],4)=>[2,2]=>[2]=>1
([(1,2),(1,3),(2,3)],4)=>[3,1]=>[1]=>0
([],5)=>[1,1,1,1,1]=>[1,1,1,1]=>0
([(3,4)],5)=>[2,1,1,1]=>[1,1,1]=>0
([(2,4),(3,4)],5)=>[3,1,1]=>[1,1]=>0
([(1,4),(2,4),(3,4)],5)=>[4,1]=>[1]=>0
([(1,4),(2,3)],5)=>[2,2,1]=>[2,1]=>2
([(1,4),(2,3),(3,4)],5)=>[4,1]=>[1]=>0
([(0,1),(2,4),(3,4)],5)=>[3,2]=>[2]=>1
([(2,3),(2,4),(3,4)],5)=>[3,1,1]=>[1,1]=>0
([(1,4),(2,3),(2,4),(3,4)],5)=>[4,1]=>[1]=>0
([(1,3),(1,4),(2,3),(2,4)],5)=>[4,1]=>[1]=>0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[4,1]=>[1]=>0
([(0,1),(2,3),(2,4),(3,4)],5)=>[3,2]=>[2]=>1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[4,1]=>[1]=>0
([],6)=>[1,1,1,1,1,1]=>[1,1,1,1,1]=>0
([(4,5)],6)=>[2,1,1,1,1]=>[1,1,1,1]=>0
([(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1]=>0
([(2,5),(3,5),(4,5)],6)=>[4,1,1]=>[1,1]=>0
([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(2,5),(3,4)],6)=>[2,2,1,1]=>[2,1,1]=>3
([(2,5),(3,4),(4,5)],6)=>[4,1,1]=>[1,1]=>0
([(1,2),(3,5),(4,5)],6)=>[3,2,1]=>[2,1]=>2
([(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>[1,1,1]=>0
([(1,5),(2,5),(3,4),(4,5)],6)=>[5,1]=>[1]=>0
([(0,1),(2,5),(3,5),(4,5)],6)=>[4,2]=>[2]=>1
([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1]=>0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(2,4),(2,5),(3,4),(3,5)],6)=>[4,1,1]=>[1,1]=>0
([(0,5),(1,5),(2,4),(3,4)],6)=>[3,3]=>[3]=>3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1]=>0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[5,1]=>[1]=>0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(0,5),(1,4),(2,3)],6)=>[2,2,2]=>[2,2]=>4
([(1,5),(2,4),(3,4),(3,5)],6)=>[5,1]=>[1]=>0
([(0,1),(2,5),(3,4),(4,5)],6)=>[4,2]=>[2]=>1
([(1,2),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>[2,1]=>2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>[4,2]=>[2]=>1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>[5,1]=>[1]=>0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]=>[2]=>1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>[3,3]=>[3]=>3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,2]=>[2]=>1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>[1,1]=>0
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[5,1]=>[1]=>0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>[3,3]=>[3]=>3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,2]=>[2]=>1
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>[1]=>0
([],7)=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1]=>0
([(5,6)],7)=>[2,1,1,1,1,1]=>[1,1,1,1,1]=>0
([(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1]=>0
([(3,6),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1]=>0
([(2,6),(3,6),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(3,6),(4,5)],7)=>[2,2,1,1,1]=>[2,1,1,1]=>4
([(3,6),(4,5),(5,6)],7)=>[4,1,1,1]=>[1,1,1]=>0
([(2,3),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1]=>3
([(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>[1,1,1,1]=>0
([(2,6),(3,6),(4,5),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,2),(3,6),(4,6),(5,6)],7)=>[4,2,1]=>[2,1]=>2
([(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1]=>0
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(3,5),(3,6),(4,5),(4,6)],7)=>[4,1,1,1]=>[1,1,1]=>0
([(1,6),(2,6),(3,5),(4,5)],7)=>[3,3,1]=>[3,1]=>5
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[6,1]=>[1]=>0
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>[4,3]=>[3]=>3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1]=>0
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,5),(3,4)],7)=>[2,2,2,1]=>[2,2,1]=>6
([(2,6),(3,5),(4,5),(4,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,2),(3,6),(4,5),(5,6)],7)=>[4,2,1]=>[2,1]=>2
([(0,3),(1,2),(4,6),(5,6)],7)=>[3,2,2]=>[2,2]=>4
([(2,3),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>[2,1,1]=>3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]=>[2]=>1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1]=>2
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]=>[2,1]=>2
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>[4,3]=>[3]=>3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>[3,3,1]=>[3,1]=>5
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2]=>1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>[4,3]=>[3]=>3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1]=>2
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>[4,3]=>[3]=>3
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>[1,1,1]=>0
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2]=>1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)=>[6,1]=>[1]=>0
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>[4,3]=>[3]=>3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>[4,3]=>[3]=>3
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>[2,2]=>4
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[5,2]=>[2]=>1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)=>[4,3]=>[3]=>3
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)=>[3,3,1]=>[3,1]=>5
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[6,1]=>[1]=>0
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>[4,3]=>[3]=>3
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>[2,1]=>2
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[6,1]=>[1]=>0
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[6,1]=>[1]=>0
([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]=>[2]=>1
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)=>[4,3]=>[3]=>3
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,3]=>[3]=>3
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,3]=>[3]=>3
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>[1,1]=>0
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[6,1]=>[1]=>0
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,3]=>[3]=>3
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>[2]=>1
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>[1]=>0
([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[5,3]=>[3]=>3
([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,1,1,1,1]=>[1,1,1,1]=>0
([(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(3,7),(4,7),(5,7),(6,7)],8)=>[5,1,1,1]=>[1,1,1]=>0
([],8)=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>0
([(4,7),(5,6)],8)=>[2,2,1,1,1,1]=>[2,1,1,1,1]=>5
([(4,7),(5,6),(6,7)],8)=>[4,1,1,1,1]=>[1,1,1,1]=>0
([(4,6),(4,7),(5,6),(5,7)],8)=>[4,1,1,1,1]=>[1,1,1,1]=>0
([(2,7),(3,7),(4,6),(5,6)],8)=>[3,3,1,1]=>[3,1,1]=>7
([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)=>[6,1,1]=>[1,1]=>0
([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[7,1]=>[1]=>0
([(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[5,1,1,1]=>[1,1,1]=>0
([(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8)=>[7,1]=>[1]=>0
([(1,6),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)=>[7,1]=>[1]=>0
([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[7,1]=>[1]=>0
([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[7,1]=>[1]=>0
([(1,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)=>[7,1]=>[1]=>0
([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)=>[3,3,1,1]=>[3,1,1]=>7
([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,1,1]=>[2,1,1]=>3
([(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>[1,1]=>0
([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,6),(1,7),(2,3),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[7,1]=>[1]=>0
([(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,3,1]=>[3,1]=>5
([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[7,1]=>[1]=>0
([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[6,1,1]=>[1,1]=>0
([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7)],8)=>[7,1]=>[1]=>0
([(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,3,1]=>[3,1]=>5
([(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,4),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>[1]=>0
([(0,7),(1,6),(2,5),(3,4)],8)=>[2,2,2,2]=>[2,2,2]=>9
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)=>[4,2,2]=>[2,2]=>4
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,2]=>[2,2]=>4
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,4]=>[4]=>6
([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8)=>[4,4]=>[4]=>6
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)=>[4,4]=>[4]=>6
([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)=>[7,1,1]=>[1,1]=>0
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)=>[9,1]=>[1]=>0
([(2,10),(3,6),(3,10),(3,13),(4,9),(4,11),(4,14),(4,15),(5,12),(5,13),(5,14),(5,15),(6,12),(6,14),(6,15),(7,8),(7,9),(7,12),(7,14),(7,15),(8,11),(8,13),(8,14),(8,15),(9,11),(9,13),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(11,15),(12,13),(13,14),(13,15)],16)=>[14,1,1]=>[1,1]=>0
([(2,9),(2,10),(2,11),(3,4),(3,5),(3,8),(3,11),(4,5),(4,7),(4,10),(5,6),(5,9),(6,7),(6,8),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12)=>[10,1,1]=>[1,1]=>0
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)=>[14,1]=>[1]=>0
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,2]=>[2,2]=>4
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,4]=>[4]=>6
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)=>[4,4]=>[4]=>6
([(3,8),(4,7),(5,6),(6,8),(7,8)],9)=>[6,1,1,1]=>[1,1,1]=>0
([(4,9),(5,8),(6,7),(7,9),(8,9)],10)=>[6,1,1,1,1]=>[1,1,1,1]=>0
([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)=>[6,1,1,1]=>[1,1,1]=>0
([(3,9),(4,5),(4,11),(5,10),(6,10),(6,11),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)=>[9,1,1,1]=>[1,1,1]=>0
([(3,11),(4,10),(5,8),(5,13),(6,9),(6,13),(7,12),(7,13),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13)],14)=>[11,1,1,1]=>[1,1,1]=>0
([(4,12),(5,11),(6,13),(6,14),(7,9),(7,14),(8,10),(8,14),(9,11),(9,13),(10,12),(10,13),(11,14),(12,14),(13,14)],15)=>[11,1,1,1,1]=>[1,1,1,1]=>0
([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)=>[7,1,1,1]=>[1,1,1]=>0
([(3,12),(3,13),(4,5),(4,13),(5,12),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(7,12),(8,9),(8,11),(8,13),(9,10),(9,12),(10,13),(11,12),(11,13),(12,13)],14)=>[11,1,1,1]=>[1,1,1]=>0
([(3,13),(4,14),(4,15),(5,6),(5,15),(6,14),(7,10),(7,11),(7,12),(7,15),(8,9),(8,11),(8,12),(8,13),(9,10),(9,12),(9,15),(10,11),(10,13),(10,14),(11,14),(11,15),(12,13),(12,14),(13,15),(14,15)],16)=>[13,1,1,1]=>[1,1,1]=>0
([(2,6),(2,10),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(7,10),(8,10),(9,10)],11)=>[9,1,1]=>[1,1]=>0
([(2,9),(3,10),(3,11),(3,12),(4,10),(4,11),(4,12),(5,6),(5,8),(5,9),(6,10),(6,11),(6,12),(7,8),(7,10),(7,11),(7,12),(8,10),(8,11),(8,12),(9,10),(9,11),(9,12)],13)=>[11,1,1]=>[1,1]=>0
([(2,9),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)=>[8,1,1]=>[1,1]=>0
([(2,9),(2,10),(2,11),(2,14),(3,6),(3,7),(3,8),(3,13),(4,6),(4,7),(4,8),(4,13),(4,14),(5,9),(5,10),(5,11),(5,13),(5,14),(6,9),(6,10),(6,11),(6,12),(6,14),(7,9),(7,10),(7,11),(7,12),(7,14),(8,9),(8,10),(8,11),(8,12),(8,14),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,13),(12,14),(13,14)],15)=>[13,1,1]=>[1,1]=>0
([(3,10),(4,9),(5,8),(5,9),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)=>[8,1,1,1]=>[1,1,1]=>0
([(3,11),(4,9),(4,14),(5,6),(5,11),(5,13),(6,12),(6,14),(7,12),(7,13),(7,14),(8,10),(8,13),(8,14),(9,10),(9,13),(10,12),(10,14),(11,12),(11,14),(12,13),(13,14)],15)=>[12,1,1,1]=>[1,1,1]=>0
([(3,8),(3,12),(4,7),(4,11),(5,9),(5,11),(5,12),(6,10),(6,11),(6,12),(7,9),(7,12),(8,10),(8,11),(9,10),(9,11),(10,12),(11,12)],13)=>[10,1,1,1]=>[1,1,1]=>0
([(5,10),(6,9),(7,8),(8,10),(9,10)],11)=>[6,1,1,1,1,1]=>[1,1,1,1,1]=>0
([(2,9),(2,13),(3,10),(3,11),(3,12),(4,10),(4,11),(4,12),(5,7),(5,8),(5,9),(5,13),(6,7),(6,10),(6,11),(6,12),(6,13),(7,10),(7,11),(7,12),(8,10),(8,11),(8,12),(8,13),(9,10),(9,11),(9,12),(10,13),(11,13),(12,13)],14)=>[12,1,1]=>[1,1]=>0
([(3,8),(4,10),(5,9),(6,7),(6,10),(7,9),(8,10),(9,10)],11)=>[8,1,1,1]=>[1,1,1]=>0
([(3,12),(4,11),(5,7),(6,8),(7,11),(8,12),(9,10),(9,11),(10,12),(11,12)],13)=>[10,1,1,1]=>[1,1,1]=>0
([(4,11),(5,10),(6,12),(7,13),(8,9),(8,12),(9,13),(10,12),(11,13),(12,13)],14)=>[10,1,1,1,1]=>[1,1,1,1]=>0
([(2,4),(2,13),(3,11),(3,12),(3,13),(4,11),(4,12),(5,8),(5,9),(5,10),(5,13),(6,8),(6,9),(6,10),(6,13),(7,8),(7,9),(7,10),(7,12),(7,13),(8,11),(8,12),(9,11),(9,12),(10,11),(10,12),(11,13),(12,13)],14)=>[12,1,1]=>[1,1]=>0
([(2,4),(2,15),(3,9),(3,15),(3,16),(4,9),(4,16),(5,11),(5,12),(5,13),(5,16),(6,11),(6,12),(6,13),(6,16),(7,10),(7,14),(7,15),(7,16),(8,11),(8,12),(8,13),(8,14),(8,16),(9,10),(9,14),(9,15),(10,11),(10,12),(10,13),(10,16),(11,14),(11,15),(12,14),(12,15),(13,14),(13,15),(14,16),(15,16)],17)=>[15,1,1]=>[1,1]=>0
([(3,8),(4,6),(4,9),(5,7),(5,9),(6,7),(6,8),(7,9),(8,9)],10)=>[7,1,1,1]=>[1,1,1]=>0
([(3,11),(3,12),(3,13),(4,6),(4,8),(4,10),(5,9),(5,11),(5,12),(5,13),(6,7),(6,8),(6,9),(7,10),(7,11),(7,12),(7,13),(8,11),(8,12),(8,13),(9,10),(9,11),(9,12),(9,13),(10,11),(10,12),(10,13)],14)=>[11,1,1,1]=>[1,1,1]=>0
([(3,4),(3,12),(4,11),(5,11),(5,12),(6,9),(6,10),(7,8),(7,10),(7,11),(8,9),(8,12),(9,10),(9,11),(10,12),(11,12)],13)=>[10,1,1,1]=>[1,1,1]=>0
([(2,5),(2,12),(2,13),(2,14),(3,4),(3,9),(3,10),(3,11),(4,12),(4,13),(4,14),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(6,12),(6,13),(6,14),(7,9),(7,10),(7,11),(7,12),(7,13),(7,14),(8,9),(8,10),(8,11),(8,12),(8,13),(8,14),(9,12),(9,13),(9,14),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14)],15)=>[13,1,1]=>[1,1]=>0
([(2,11),(3,7),(3,11),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)=>[10,1,1]=>[1,1]=>0
([(0,3),(1,2),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,4]=>[4]=>6
([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)=>[4,4]=>[4]=>6
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(6,7)],8)=>[4,4]=>[4]=>6
([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)=>[4,4]=>[4]=>6
([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8)=>[4,4]=>[4]=>6
([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)=>[4,4]=>[4]=>6
([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)=>[4,4]=>[4]=>6
([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[6,2]=>[2]=>1
([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8)=>[5,3]=>[3]=>3
([(0,1),(2,7),(3,7),(4,6),(5,6),(6,7)],8)=>[6,2]=>[2]=>1
([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[6,2]=>[2]=>1
([(0,6),(1,6),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7)],8)=>[5,3]=>[3]=>3
([(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[5,3]=>[3]=>3
([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>[2]=>1
([(0,6),(1,7),(2,7),(3,4),(3,5),(4,5),(6,7)],8)=>[5,3]=>[3]=>3
([(0,1),(0,2),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[5,3]=>[3]=>3
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[5,3]=>[3]=>3
([(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7)],9)=>[8,1]=>[1]=>0
([(0,7),(1,6),(2,3),(2,4),(3,4),(5,6),(5,7)],8)=>[5,3]=>[3]=>3
([(0,1),(0,2),(1,2),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[5,3]=>[3]=>3
([(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[5,3]=>[3]=>3
([(0,1),(0,2),(1,2),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[5,3]=>[3]=>3
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Description
The Gini index of an integer partition.
As discussed in [1], this statistic is equal to St000567The sum of the products of all pairs of parts. applied to the conjugate partition.
As discussed in [1], this statistic is equal to St000567The sum of the products of all pairs of parts. applied to the conjugate partition.
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first row removal
Description
Removes the first entry of an integer partition
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
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