Identifier
Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00160: Permutations graph of inversionsGraphs
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]=>[2,1,3]=>([(1,2)],3)=>([(0,1)],2) [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]=>[1,3,2]=>([(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]=>[2,1,4,3]=>([(0,3),(1,2)],4)=>([(0,1)],2) [1,0,1,0,1,1,0,0]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>([(0,1)],2) [1,0,1,1,0,0,1,0]=>[2,1,3,4]=>([(2,3)],4)=>([(0,1)],2) [1,0,1,1,0,1,0,0]=>[2,3,1,4]=>([(1,3),(2,3)],4)=>([(0,1)],2) [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]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)=>([(0,1)],2) [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]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>([(0,1)],2) [1,1,0,1,0,1,0,0]=>[1,3,2,4]=>([(2,3)],4)=>([(0,1)],2) [1,1,0,1,1,0,0,0]=>[1,3,4,2]=>([(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]=>[1,4,2,3]=>([(1,3),(2,3)],4)=>([(0,1)],2) [1,1,1,0,1,0,0,0]=>[1,2,4,3]=>([(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]=>[2,1,4,3,5]=>([(1,4),(2,3)],5)=>([(0,1)],2) [1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>([(0,1),(2,4),(3,4)],5)=>([(0,1)],2) [1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)=>([(0,1)],2) [1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,1)],2) [1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>([(0,1),(2,4),(3,4)],5)=>([(0,1)],2) [1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>([(1,4),(2,3)],5)=>([(0,1)],2) [1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>([(0,1),(2,4),(3,4)],5)=>([(0,1)],2) [1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>([(3,4)],5)=>([(0,1)],2) [1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)=>([(0,1)],2) [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]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2) [1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,1)],2) [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]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)=>([(0,1)],2) [1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,1)],2) [1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>([(0,1),(2,4),(3,4)],5)=>([(0,1)],2) [1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>([(1,4),(2,3)],5)=>([(0,1)],2) [1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>([(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>([(0,1)],2) [1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>([(3,4)],5)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>([(2,4),(3,4)],5)=>([(0,1)],2) [1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>([(1,4),(2,4),(3,4)],5)=>([(0,1)],2) [1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,1)],2) [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]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>([(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>([(2,4),(3,4)],5)=>([(0,1)],2) [1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>([(3,4)],5)=>([(0,1)],2) [1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>([(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]=>[1,5,2,3,4]=>([(1,4),(2,4),(3,4)],5)=>([(0,1)],2) [1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>([(2,4),(3,4)],5)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>([(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]=>[2,1,4,3,6,5]=>([(0,5),(1,4),(2,3)],6)=>([(0,1)],2) [1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>([(0,1)],2) [1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>([(2,5),(3,4)],6)=>([(0,1)],2) [1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>([(1,5),(2,4),(3,4),(3,5)],6)=>([(0,1)],2) [1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>([(2,5),(3,4)],6)=>([(0,1)],2) [1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,1)],2) [1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,1)],2) [1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>([(2,5),(3,4)],6)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>([(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [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]=>[3,1,4,2,6,5]=>([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [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]=>[3,1,5,2,6,4]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>([(0,1)],2) [1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>([(2,5),(3,4)],6)=>([(0,1)],2) [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>([(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,1)],2) [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>([(1,5),(2,4),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,1)],2) [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>([(2,5),(3,4)],6)=>([(0,1)],2) [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>([(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>([(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [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]=>[4,1,5,2,3,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>([(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>([(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]=>[4,1,6,2,3,5]=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>([(1,5),(2,4),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>([(2,5),(3,4)],6)=>([(0,1)],2) [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>([(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>([(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>([(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>([(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,0,0,1,1,0,0]=>[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]=>[5,1,2,6,3,4]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>([(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]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>([(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>([(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>([(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>([(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]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>([(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>([(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 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
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.
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].