Identifier
Mp00199: Dyck paths prime Dyck pathDyck paths
Mp00025: Dyck paths to 132-avoiding permutationPermutations
Mp00066: Permutations inversePermutations
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,1,0,0]=>[1,2]=>[1,2] [1,0,1,0]=>[1,1,0,1,0,0]=>[2,1,3]=>[2,1,3] [1,1,0,0]=>[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3] [1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[3,2,1,4] [1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,1,2,4] [1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[2,3,1,4] [1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4] [1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4] [1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[4,3,2,1,5] [1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[4,3,1,2,5] [1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[4,2,3,1,5] [1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[4,2,1,3,5] [1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,1,2,3,5] [1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[3,4,2,1,5] [1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[3,4,1,2,5] [1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[3,2,4,1,5] [1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,2,1,4,5] [1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[3,1,2,4,5] [1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[2,3,4,1,5] [1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[2,3,1,4,5] [1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5] [1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5] [1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6] [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6] [1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[5,4,2,3,1,6] [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6] [1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6] [1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[5,3,4,2,1,6] [1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[5,3,4,1,2,6] [1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[5,3,2,4,1,6] [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6] [1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6] [1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[5,2,3,4,1,6] [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[5,2,3,1,4,6] [1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6] [1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6] [1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6] [1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[4,5,3,1,2,6] [1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[4,5,2,3,1,6] [1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[4,5,2,1,3,6] [1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[4,5,1,2,3,6] [1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6] [1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[4,3,5,1,2,6] [1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6] [1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6] [1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6] [1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[4,2,3,5,1,6] [1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[4,2,3,1,5,6] [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6] [1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6] [1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6] [1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[3,4,5,1,2,6] [1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6] [1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6] [1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6] [1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6] [1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6] [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6] [1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6] [1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6] [1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6] [1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6] [1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6] [1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[6,5,4,2,3,1,7] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[6,5,3,4,2,1,7] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[6,5,3,4,1,2,7] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[6,5,3,2,4,1,7] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[6,5,2,3,4,1,7] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[6,5,2,3,1,4,7] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[6,4,5,3,2,1,7] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[6,4,5,3,1,2,7] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[6,4,5,2,3,1,7] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[6,4,5,2,1,3,7] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[6,4,5,1,2,3,7] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[6,4,3,5,2,1,7] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[6,4,3,5,1,2,7] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[6,4,3,2,5,1,7] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[6,4,2,3,5,1,7] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[6,4,2,3,1,5,7] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[6,3,4,5,2,1,7] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[6,3,4,5,1,2,7] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[6,3,4,2,5,1,7] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[6,3,4,2,1,5,7] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[6,3,4,1,2,5,7] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[6,3,2,4,5,1,7] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[6,3,2,4,1,5,7] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[6,2,3,4,5,1,7] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[6,2,3,4,1,5,7] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[6,2,3,1,4,5,7] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7] [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7] [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[5,6,4,3,1,2,7] [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[5,6,4,2,3,1,7] [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[5,6,4,2,1,3,7] [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[5,6,4,1,2,3,7] [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[5,6,3,4,2,1,7] [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7] [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[5,6,3,2,4,1,7] [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[5,6,3,2,1,4,7] [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[5,6,3,1,2,4,7] [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[5,6,2,3,4,1,7] [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[5,6,2,3,1,4,7] [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[5,6,2,1,3,4,7] [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[5,6,1,2,3,4,7] [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7] [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[5,4,6,3,1,2,7] [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[5,4,6,2,3,1,7] [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[5,4,6,2,1,3,7] [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[5,4,6,1,2,3,7] [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7] [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[5,4,3,6,1,2,7] [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7] [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7] [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7] [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[5,4,2,3,6,1,7] [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[5,4,2,3,1,6,7] [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7] [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7] [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[5,3,4,6,2,1,7] [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[5,3,4,6,1,2,7] [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[5,3,4,2,6,1,7] [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[5,3,4,2,1,6,7] [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[5,3,4,1,2,6,7] [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[5,3,2,4,6,1,7] [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[5,3,2,4,1,6,7] [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7] [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7] [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[5,2,3,4,6,1,7] [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[5,2,3,4,1,6,7] [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[5,2,3,1,4,6,7] [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7] [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7] [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7] [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[4,5,6,3,1,2,7] [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[4,5,6,2,3,1,7] [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[4,5,6,2,1,3,7] [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3,7] [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7] [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[4,5,3,6,1,2,7] [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7] [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7] [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[4,5,3,1,2,6,7] [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[4,5,2,3,6,1,7] [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[4,5,2,3,1,6,7] [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[4,5,2,1,3,6,7] [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[4,5,1,2,3,6,7] [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7] [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[4,3,5,6,1,2,7] [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7] [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7] [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,3,5,1,2,6,7] [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7] [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7] [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7] [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7] [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[4,2,3,5,6,1,7] [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[4,2,3,5,1,6,7] [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[4,2,3,1,5,6,7] [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7] [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7] [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7] [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[3,4,5,6,1,2,7] [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7] [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7] [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[3,4,5,1,2,6,7] [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7] [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7] [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7] [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6,7] [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7] [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7] [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7] [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7] [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7] [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7] [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7] [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7] [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7] [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[7,6,5,3,4,2,1,8] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[7,6,4,5,2,3,1,8] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,5,2,1,8] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,2,5,1,8] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[7,6,3,4,5,2,1,8] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[7,5,6,4,3,1,2,8] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[7,5,4,6,2,1,3,8] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[7,4,5,6,1,2,3,8] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[7,4,5,2,3,6,1,8] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[6,5,7,4,2,1,3,8] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,1,7,8]=>[6,2,3,1,4,5,7,8] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[5,6,7,1,2,3,4,8] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[5,6,4,3,7,2,1,8] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[5,3,4,1,2,6,7,8] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[5,2,3,4,1,6,7,8] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[4,5,6,7,1,2,3,8] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[4,5,6,1,2,3,7,8] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,1,4,5,7,8]=>[4,2,3,5,6,1,7,8] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[3,4,5,6,7,1,2,8] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[3,4,5,2,6,1,7,8] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[3,4,1,2,5,6,7,8] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9] [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,3,2,1,9]=>[8,7,6,4,5,3,2,1,9] [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[7,8,6,5,4,3,2,1,9] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9] [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9] [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9] [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,1,2,3,4,5,7,8,9] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[5,6,7,8,1,2,3,4,9] [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9] [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9] [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[4,5,6,1,2,3,7,8,9] [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9] [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9] [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9] [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9] [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9] [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10] [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10] [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[8,1,2,3,4,5,6,7,9,10] [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10] [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10] [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10] [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10] [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[5,6,7,8,1,2,3,4,9,10] [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10] [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10] [1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[4,5,6,1,2,3,7,8,9,10] [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10] [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10] [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10] [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10] [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10] [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11] [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
inverse
Description
Sends a permutation to its inverse.