Identifier
Mp00201:
Dyck paths
—Ringel⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Mp00065: Permutations —permutation poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Images
=>
Cc0005;cc-rep-0Cc0014;cc-rep-2Cc0014;cc-rep-3
[1,0]=>[2,1]=>([],2)=>([],2)
[1,0,1,0]=>[3,1,2]=>([(1,2)],3)=>([(1,2)],3)
[1,1,0,0]=>[2,3,1]=>([(1,2)],3)=>([(1,2)],3)
[1,0,1,0,1,0]=>[4,1,2,3]=>([(1,2),(2,3)],4)=>([(1,2),(2,3)],4)
[1,0,1,1,0,0]=>[3,1,4,2]=>([(0,3),(1,2),(1,3)],4)=>([(0,3),(1,2),(1,3)],4)
[1,1,0,0,1,0]=>[2,4,1,3]=>([(0,3),(1,2),(1,3)],4)=>([(0,3),(1,2),(1,3)],4)
[1,1,0,1,0,0]=>[4,3,1,2]=>([(2,3)],4)=>([(2,3)],4)
[1,1,1,0,0,0]=>[2,3,4,1]=>([(1,2),(2,3)],4)=>([(1,2),(2,3)],4)
[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5)=>([(1,4),(3,2),(4,3)],5)
[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>([(0,4),(1,2),(2,3),(2,4)],5)=>([(0,4),(1,2),(1,4),(4,3)],5)
[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>([(1,3),(1,4),(4,2)],5)=>([(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>([(0,4),(1,2),(1,4),(4,3)],5)=>([(0,4),(1,2),(2,3),(2,4)],5)
[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>([(0,4),(1,2),(1,4),(4,3)],5)=>([(0,4),(1,2),(2,3),(2,4)],5)
[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>([(1,4),(2,3),(3,4)],5)=>([(1,3),(1,4),(4,2)],5)
[1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>([(2,3),(3,4)],5)=>([(2,3),(3,4)],5)
[1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>([(0,4),(1,4),(2,3),(2,4)],5)=>([(0,4),(1,2),(1,3),(1,4)],5)
[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>([(0,4),(1,2),(2,3),(2,4)],5)=>([(0,4),(1,2),(1,4),(4,3)],5)
[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>([(0,4),(1,2),(1,3),(1,4)],5)=>([(0,4),(1,4),(2,3),(2,4)],5)
[1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>([(1,4),(2,3)],5)=>([(1,4),(2,3)],5)
[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5)=>([(1,4),(3,2),(4,3)],5)
[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6)=>([(1,5),(3,4),(4,2),(5,3)],6)
[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
[1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>([(1,5),(4,3),(5,2),(5,4)],6)=>([(1,5),(2,3),(3,5),(5,4)],6)
[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>([(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>([(1,3),(1,5),(4,2),(5,4)],6)=>([(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
[1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>([(1,4),(1,5),(4,3),(5,2)],6)=>([(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
[1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>([(1,5),(2,3),(3,5),(5,4)],6)=>([(1,5),(4,3),(5,2),(5,4)],6)
[1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>([(1,5),(2,3),(3,4),(4,5)],6)=>([(1,3),(1,5),(4,2),(5,4)],6)
[1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>([(0,5),(1,3),(4,2),(5,4)],6)=>([(0,5),(1,3),(4,2),(5,4)],6)
[1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>([(0,5),(1,5),(2,3),(3,4),(3,5)],6)=>([(0,5),(1,2),(1,3),(1,5),(5,4)],6)
[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
[1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>([(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>([(1,5),(2,3),(2,5),(3,4)],6)=>([(1,4),(2,3),(2,5),(4,5)],6)
[1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>([(0,5),(1,5),(2,3),(2,5),(5,4)],6)=>([(0,5),(1,4),(4,2),(4,3),(4,5)],6)
[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
[1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)
[1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>([(0,5),(1,2),(1,3),(1,5),(5,4)],6)=>([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
[1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>([(1,4),(2,3),(3,5),(4,5)],6)=>([(1,4),(1,5),(4,3),(5,2)],6)
[1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>([(1,4),(2,3),(2,5),(4,5)],6)=>([(1,5),(2,3),(2,5),(3,4)],6)
[1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>([(3,4),(4,5)],6)=>([(3,4),(4,5)],6)
[1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>([(0,5),(1,4),(2,3),(2,5),(4,5)],6)=>([(0,5),(1,3),(1,4),(1,5),(4,2)],6)
[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>([(0,5),(1,4),(4,2),(4,3),(4,5)],6)=>([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>([(0,5),(1,3),(1,4),(1,5),(4,2)],6)=>([(0,5),(1,4),(2,3),(2,5),(4,5)],6)
[1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>([(1,3),(2,4),(4,5)],6)=>([(1,3),(2,4),(4,5)],6)
[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6)=>([(1,5),(3,4),(4,2),(5,3)],6)
[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)
[1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7)=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)
[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)=>([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7)=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>([(0,6),(1,5),(3,6),(4,2),(4,6),(5,3),(5,4)],7)=>([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7)
[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)
[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>([(0,3),(1,4),(1,5),(1,6),(2,6),(3,2),(3,4),(3,5)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7)
[1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>([(1,6),(4,3),(5,2),(6,4),(6,5)],7)=>([(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)
[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)
[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)
[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
[1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7)=>([(0,5),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(5,4)],7)
[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)
[1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)=>([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>([(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)=>([(0,5),(0,6),(1,2),(1,5),(1,6),(3,4),(5,3),(6,4)],7)
[1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)=>([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],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),(3,4),(4,2),(5,3)],7)=>([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
[1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>([(0,6),(1,3),(1,4),(3,6),(4,5),(5,2),(5,6)],7)=>([(0,6),(1,2),(1,4),(1,6),(3,5),(4,5),(6,3)],7)
[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>([(0,5),(0,6),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)=>([(0,2),(0,4),(0,6),(1,4),(1,5),(1,6),(2,5),(5,3),(6,3)],7)
[1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>([(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)=>([(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7)=>([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>([(0,6),(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)=>([(0,6),(1,4),(3,5),(4,2),(4,3),(4,6),(6,5)],7)
[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)
[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)
[1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>([(0,2),(0,4),(0,6),(1,4),(1,5),(1,6),(2,5),(5,3),(6,3)],7)=>([(0,5),(0,6),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(4,2)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7)
[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7)=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>([(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7)=>([(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7)
[1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>([(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)=>([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)=>([(0,6),(1,2),(1,4),(1,6),(3,5),(4,3),(6,5)],7)
[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)
[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7)=>([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(6,2)],7)=>([(0,5),(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>([(1,5),(1,6),(4,3),(5,4),(6,2)],7)=>([(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>([(0,6),(1,3),(1,6),(5,2),(6,4),(6,5)],7)=>([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7)
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(3,4),(5,3),(6,4)],7)=>([(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(4,2),(6,4)],7)=>([(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)=>([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7)
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(5,4),(6,3)],7)=>([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)
[1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7)=>([(0,6),(1,3),(1,6),(5,2),(6,4),(6,5)],7)
[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(5,4)],7)=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7)
[1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)=>([(0,5),(0,6),(1,4),(4,3),(4,5),(4,6),(6,2)],7)
[1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
[1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>([(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,3),(1,5),(1,6),(4,2),(6,4)],7)
[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)=>([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>([(2,6),(4,5),(5,3),(6,4)],7)=>([(2,6),(4,5),(5,3),(6,4)],7)
[1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)=>([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7)=>([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(4,2)],7)
[1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>([(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7)=>([(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7)
[1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>([(0,5),(1,3),(1,6),(4,2),(5,4),(5,6)],7)=>([(0,5),(1,5),(1,6),(2,3),(3,6),(6,4)],7)
[1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7)=>([(0,6),(1,5),(5,2),(5,3),(5,6),(6,4)],7)
[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7)=>([(0,3),(1,4),(1,5),(1,6),(2,6),(3,2),(3,4),(3,5)],7)
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7)=>([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3)],7)
[1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>([(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)=>([(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>([(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7)=>([(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7)
[1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)=>([(0,2),(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(6,4)],7)
[1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>([(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>([(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)=>([(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>([(0,4),(1,3),(1,6),(5,2),(6,5)],7)=>([(0,6),(1,3),(2,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>([(0,6),(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7)=>([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7)
[1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)=>([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7)
[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>([(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7)=>([(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>([(1,6),(2,3),(2,6),(3,5),(6,4)],7)=>([(1,3),(2,4),(3,6),(4,5),(4,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7)=>([(0,6),(1,4),(4,5),(5,2),(5,3),(5,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)
[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)
[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)
[1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>([(0,5),(0,6),(1,4),(4,3),(4,5),(4,6),(6,2)],7)=>([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)
[1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7)=>([(0,6),(1,5),(3,6),(4,2),(4,6),(5,3),(5,4)],7)
[1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>([(0,6),(1,2),(1,4),(1,6),(3,5),(4,5),(6,3)],7)=>([(0,6),(1,3),(1,4),(3,6),(4,5),(5,2),(5,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)
[1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7)=>([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7)
[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>([(0,2),(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(6,4)],7)=>([(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(4,5),(6,2)],7)=>([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>([(0,5),(0,6),(1,2),(1,3),(1,5),(2,6),(3,6),(6,4)],7)=>([(0,5),(0,6),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5)],7)
[1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>([(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(1,6),(4,3),(5,2),(6,4),(6,5)],7)
[1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,2),(1,5),(1,6),(5,4),(6,3)],7)
[1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)=>([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>([(0,5),(1,5),(1,6),(2,3),(3,6),(6,4)],7)=>([(0,5),(1,3),(1,6),(4,2),(5,4),(5,6)],7)
[1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,3),(1,4),(1,6),(4,5),(6,2)],7)
[1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>([(0,6),(1,3),(2,4),(4,5),(5,6)],7)=>([(0,4),(1,3),(1,6),(5,2),(6,5)],7)
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>([(1,6),(2,4),(5,3),(6,5)],7)=>([(1,6),(2,4),(5,3),(6,5)],7)
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7)=>([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7)
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>([(0,5),(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(6,2)],7)
[1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>([(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7)
[1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)=>([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)
[1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>([(1,6),(2,6),(3,4),(3,6),(4,5)],7)=>([(1,5),(2,3),(2,4),(2,6),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>([(0,6),(1,4),(2,3),(2,6),(4,6),(6,5)],7)=>([(0,6),(1,5),(4,3),(5,2),(5,4),(5,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)
[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)
[1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>([(0,6),(1,4),(3,5),(4,2),(4,3),(4,6),(6,5)],7)=>([(0,6),(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
[1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>([(0,6),(1,5),(5,2),(5,3),(5,6),(6,4)],7)=>([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7)
[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>([(0,5),(0,6),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5)],7)=>([(0,5),(0,6),(1,2),(1,3),(1,5),(2,6),(3,6),(6,4)],7)
[1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>([(0,6),(1,2),(1,4),(1,6),(3,5),(4,3),(6,5)],7)=>([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)
[1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7)=>([(0,6),(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7)=>([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,2)],7)=>([(0,5),(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,2)],7)
[1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>([(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(1,5),(1,6),(4,3),(5,4),(6,2)],7)
[1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>([(1,3),(2,4),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
[1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>([(1,5),(2,3),(2,4),(2,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,6),(4,5)],7)
[1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>([(2,4),(3,5),(5,6)],7)=>([(2,4),(3,5),(5,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>([(0,6),(1,4),(2,3),(2,6),(4,5),(5,6)],7)=>([(0,6),(1,3),(1,5),(1,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>([(0,6),(1,4),(4,5),(5,2),(5,3),(5,6)],7)=>([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7)
[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>([(0,6),(1,5),(4,3),(5,2),(5,4),(5,6)],7)=>([(0,6),(1,4),(2,3),(2,6),(4,6),(6,5)],7)
[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>([(0,6),(1,3),(1,5),(1,6),(4,2),(5,4)],7)=>([(0,6),(1,4),(2,3),(2,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>([(1,6),(2,4),(5,3),(6,5)],7)=>([(1,6),(2,4),(5,3),(6,5)],7)
[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,1,2,3,7,4,5,6]=>([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)=>([(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)=>([(0,3),(0,7),(1,6),(1,7),(3,4),(3,6),(5,2),(6,5),(7,4),(7,5)],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),(1,6),(3,5),(4,3),(5,2),(6,4),(6,7)],8)=>([(0,6),(1,4),(1,7),(2,7),(5,2),(6,5),(7,3)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>([(0,5),(0,6),(0,7),(1,4),(3,7),(4,3),(4,5),(4,6),(7,2)],8)=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,5),(3,7),(5,6),(6,4)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,1,2,7,6,3,8,5]=>([(0,3),(1,4),(1,5),(1,6),(2,6),(2,7),(3,2),(3,4),(3,5),(4,7),(5,7)],8)=>([(0,5),(0,6),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,7),(7,2)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>([(0,3),(0,7),(1,6),(1,7),(3,4),(3,6),(5,2),(6,5),(7,4),(7,5)],8)=>([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8)=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(4,7),(5,2),(5,7),(6,7)],8)=>([(0,6),(1,2),(1,3),(1,6),(2,5),(2,7),(3,4),(3,7),(5,4),(6,5),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>([(0,6),(0,7),(1,3),(1,4),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6)],8)=>([(0,3),(0,6),(1,4),(1,6),(1,7),(2,5),(3,4),(3,7),(4,2),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>([(0,6),(0,7),(1,3),(1,4),(2,6),(3,6),(3,7),(4,5),(5,2),(5,7)],8)=>([(0,3),(0,6),(0,7),(1,4),(1,6),(1,7),(2,5),(3,4),(4,2),(7,5)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,4,2,8,3,6,7]=>([(0,6),(0,7),(1,4),(1,5),(3,7),(4,6),(4,7),(5,3),(5,6),(7,2)],8)=>([(0,3),(1,5),(1,6),(1,7),(2,7),(3,2),(3,5),(3,6),(6,4),(7,4)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>([(0,6),(0,7),(1,2),(1,4),(2,6),(2,7),(3,5),(3,6),(4,3),(4,7),(7,5)],8)=>([(0,2),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(5,3),(6,3),(7,5)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>([(0,7),(1,3),(1,4),(2,5),(2,7),(3,5),(3,6),(4,2),(4,6),(6,7)],8)=>([(0,2),(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>([(1,3),(1,5),(2,6),(3,6),(3,7),(4,2),(5,4),(5,7)],8)=>([(1,5),(1,6),(2,3),(2,5),(3,4),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]=>([(0,7),(1,3),(1,5),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7)],8)=>([(0,7),(1,3),(1,4),(1,7),(2,6),(4,2),(4,5),(5,6),(7,5)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>([(0,3),(0,6),(0,7),(1,4),(1,6),(1,7),(2,5),(3,4),(4,2),(7,5)],8)=>([(0,6),(0,7),(1,3),(1,4),(2,6),(3,6),(3,7),(4,5),(5,2),(5,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]=>([(0,6),(0,7),(1,4),(1,7),(4,6),(5,3),(6,5),(7,2)],8)=>([(0,5),(1,3),(2,6),(3,6),(3,7),(4,2),(4,7),(5,4)],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),(1,3),(1,6),(1,7),(4,5),(5,2),(6,4)],8)=>([(0,7),(1,6),(2,4),(2,7),(3,7),(5,3),(6,5)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>([(1,6),(1,7),(4,5),(5,3),(6,4),(7,2)],8)=>([(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,8,1,3,7,4,5,6]=>([(0,7),(1,3),(1,7),(5,2),(6,5),(7,4),(7,6)],8)=>([(0,7),(1,6),(2,4),(4,5),(5,7),(7,3),(7,6)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8)=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>([(0,3),(0,7),(1,6),(1,7),(3,4),(3,6),(5,2),(6,5),(7,4),(7,5)],8)=>([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(7,5)],8)=>([(0,5),(1,3),(1,7),(2,6),(2,7),(3,6),(4,2),(5,4)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[8,3,1,2,7,4,5,6]=>([(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)=>([(1,6),(1,7),(2,4),(4,5),(5,6),(5,7),(7,3)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>([(0,5),(1,3),(2,6),(3,6),(3,7),(4,2),(4,7),(5,4)],8)=>([(0,6),(0,7),(1,4),(1,7),(4,6),(5,3),(6,5),(7,2)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,5),(3,7),(5,6),(6,4)],8)=>([(0,5),(0,6),(0,7),(1,4),(3,7),(4,3),(4,5),(4,6),(7,2)],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),(1,3),(1,6),(1,7),(2,6),(4,2),(5,4),(5,7)],8)=>([(0,7),(1,6),(1,7),(2,3),(2,7),(3,5),(5,6),(6,4)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>([(1,3),(1,7),(2,6),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)=>([(1,3),(1,7),(2,6),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>([(1,5),(1,6),(2,3),(2,5),(3,4),(4,6),(5,7),(6,7)],8)=>([(1,3),(1,5),(2,6),(3,6),(3,7),(4,2),(5,4),(5,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>([(0,7),(1,6),(1,7),(2,3),(2,7),(3,5),(5,6),(6,4)],8)=>([(0,5),(1,3),(1,6),(1,7),(2,6),(4,2),(5,4),(5,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>([(2,4),(2,7),(5,6),(6,3),(7,5)],8)=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,1,8,7,2,5,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,7),(7,4)],8)=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,4),(3,6),(3,7),(4,5)],8)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>([(1,5),(1,6),(2,4),(2,5),(3,7),(4,6),(5,3),(6,7)],8)=>([(1,4),(1,5),(2,6),(3,6),(3,7),(4,3),(5,2),(5,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>([(1,6),(1,7),(2,4),(2,6),(4,7),(6,3),(6,5),(7,5)],8)=>([(1,5),(2,3),(2,5),(3,4),(3,7),(4,6),(5,6),(5,7)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>([(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,7),(7,4)],8)=>([(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(4,7),(5,6)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]=>([(0,2),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(7,4)],8)=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(5,4),(6,5)],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),(1,2),(1,3),(1,6),(2,5),(2,7),(3,4),(3,7),(5,4),(6,5),(6,7)],8)=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(4,7),(5,2),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3,4,1,2,7,8,5]=>([(0,7),(1,5),(2,4),(4,6),(4,7),(5,6),(5,7),(7,3)],8)=>([(0,6),(0,7),(1,5),(5,2),(5,6),(5,7),(6,4),(7,3)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>([(0,7),(1,4),(2,3),(2,5),(3,6),(3,7),(4,5),(5,6),(5,7)],8)=>([(0,6),(0,7),(1,3),(1,6),(1,7),(4,2),(6,5),(7,4),(7,5)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(4,6),(4,7),(6,3)],8)=>([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(4,6),(4,7),(6,3)],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),(1,6),(2,4),(2,7),(3,7),(5,3),(6,5)],8)=>([(0,7),(1,3),(1,6),(1,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)=>([(2,4),(2,7),(5,6),(6,3),(7,5)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8)=>([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>([(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(4,7),(5,6)],8)=>([(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,7),(7,4)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8)=>([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>([(2,4),(3,5),(5,6),(6,7)],8)=>([(2,4),(3,5),(5,6),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>([(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)=>([(1,6),(1,7),(4,5),(5,3),(6,4),(7,2)],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),(1,3),(1,6),(1,7),(4,5),(5,2),(6,4)],8)=>([(0,7),(1,6),(2,4),(2,7),(3,7),(5,3),(6,5)],8)
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
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