Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Images
=>
Cc0005;cc-rep-0Cc0020;cc-rep-2Cc0020;cc-rep-3
[1,0]=>[1]=>([],1)=>([],1)
[1,0,1,0]=>[2,1]=>([(0,1)],2)=>([(0,1)],2)
[1,1,0,0]=>[1,2]=>([],2)=>([],1)
[1,0,1,0,1,0]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,0,0]=>[2,3,1]=>([(0,2),(1,2)],3)=>([(0,1)],2)
[1,1,0,0,1,0]=>[3,1,2]=>([(0,2),(1,2)],3)=>([(0,1)],2)
[1,1,0,1,0,0]=>[2,1,3]=>([(1,2)],3)=>([(0,1)],2)
[1,1,1,0,0,0]=>[1,2,3]=>([],3)=>([],1)
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)=>([(0,1)],2)
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,1)],2)
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>([(1,3),(2,3)],4)=>([(0,1)],2)
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>([(0,1)],2)
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>([(0,1)],2)
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>([(2,3)],4)=>([(0,1)],2)
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>([],4)=>([],1)
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2)
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2)
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)=>([(0,1)],2)
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2)
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2)
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)=>([(0,1)],2)
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2)
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>([(0,1)],2)
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>([(0,1)],2)
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>([(3,4)],5)=>([(0,1)],2)
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>([],5)=>([],1)
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,1,0,0,0,1,0]=>[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)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)
[1,1,1,0,0,0,1,0,1,0,1,0]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,1)],2)
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,1,1,0,0,0,1,0]=>[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)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2)
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)=>([(0,1)],2)
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2)
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>([(0,1)],2)
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>([(4,5)],6)=>([(0,1)],2)
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>([],6)=>([],1)
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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
core
Description
The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
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