Identifier
Mp00201:
Dyck paths
—Ringel⟶
Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0020;cc-rep-2Cc0002;cc-rep-3
[1,0]=>[2,1]=>([(0,1)],2)=>[2]
[1,0,1,0]=>[3,1,2]=>([(0,2),(1,2)],3)=>[3]
[1,1,0,0]=>[2,3,1]=>([(0,2),(1,2)],3)=>[3]
[1,0,1,0,1,0]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[4]
[1,0,1,1,0,0]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)=>[4]
[1,1,0,0,1,0]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[4]
[1,1,0,1,0,0]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]
[1,1,1,0,0,0]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)=>[4]
[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[5]
[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[5]
[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[5]
[1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]
[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[5]
[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[5]
[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)=>[5]
[1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]
[1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]
[1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>[5]
[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[5]
[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>[5]
[1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[5]
[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[5]
[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[6]
[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[6]
[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[6]
[1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[6]
[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[6]
[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[6]
[1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[6]
[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>[6]
[1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[6]
[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[6]
[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[6]
[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[6]
[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[6]
[1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>[6]
[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[6]
[1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>[6]
[1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[6]
[1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[6]
[1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[6]
[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[6]
[1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[6]
[1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[6]
[1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[6]
[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]
[1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[6]
[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[7]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[7]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[7]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[7]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[7]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[7]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[7]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7)=>[7]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[7]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[7]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[7]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[7]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>[7]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[7]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[7]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>([(0,6),(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)=>[7]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>([(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>([(0,1),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[7]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[7]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[7]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[7]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[7]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[7]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[7]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[7]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[7]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>[7]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7)=>[7]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>([(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[7]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[7]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[7]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>([(0,4),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>([(0,4),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>([(0,6),(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)=>[7]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>([(0,3),(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)=>[7]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>([(0,1),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[7]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[7]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>([(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>([(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>([(0,3),(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)=>[7]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[7]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(0,6),(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)=>[7]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[7]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[7]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[7]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[7]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[7]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,1,2,3,7,4,5,6]=>([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)=>[8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>([(0,4),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[8,1,2,7,6,3,4,5]=>([(0,7),(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)=>[8]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)=>[8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)=>[8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>([(0,6),(1,4),(2,4),(2,7),(3,5),(3,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>([(0,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)=>[8]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>([(0,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[8]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>([(0,7),(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)=>[8]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[8,1,4,2,6,7,3,5]=>([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>([(0,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]=>([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)=>[8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]=>([(0,7),(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),(6,7)],8)=>[8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>([(0,7),(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)=>[8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)=>[8]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)=>[8]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,8,1,7,6,3,4,5]=>([(0,1),(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)=>[8]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,3,1,2,4,8,5,7]=>([(0,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)=>[8]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)=>[8]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>([(0,4),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[8]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]=>([(0,5),(0,7),(1,5),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[8]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,1,2,6,3,4,5]=>([(0,6),(0,7),(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)=>[8]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[8]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>([(0,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>([(0,7),(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)=>[8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>([(0,5),(0,7),(1,5),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>([(0,6),(0,7),(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)=>[8]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>([(0,6),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>([(0,3),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]=>([(0,6),(1,4),(2,4),(2,7),(3,5),(3,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3,4,1,2,7,8,5]=>([(0,6),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,7),(5,7),(6,7)],8)=>[8]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>([(0,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,3,7,1,2,4,8,5]=>([(0,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[8]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]=>([(0,7),(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),(6,7)],8)=>[8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>([(0,6),(0,7),(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)=>[8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>([(0,5),(0,6),(0,7),(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)=>[8]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>([(0,3),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>([(0,5),(0,6),(0,7),(1,4),(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)],8)=>[8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>([(0,4),(0,5),(0,6),(0,7),(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)=>[8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>([(0,7),(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)=>[8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,4,5,6,7,1,3]=>([(0,7),(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),(6,7)],8)=>[8]
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
searching the database
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