Identifier
Mp00199: Dyck paths prime Dyck pathDyck paths
Mp00023: Dyck paths to non-crossing permutationPermutations
Mp00066: Permutations inversePermutations
Mp00127: Permutations left-to-right-maxima to Dyck path Dyck paths
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-4
[1,0]=>[1,1,0,0]=>[2,1]=>[2,1]=>[1,1,0,0] [1,0,1,0]=>[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[1,1,1,0,0,0] [1,1,0,0]=>[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[1,1,1,0,0,0] [1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[1,1,1,1,0,0,0,0] [1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,1,3,2]=>[1,1,1,1,0,0,0,0] [1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0] [1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0] [1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0] [1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0] [1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,1,2,4,3]=>[1,1,1,1,1,0,0,0,0,0] [1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,1,3,2,4]=>[1,1,1,1,1,0,0,0,0,0] [1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[5,1,3,4,2]=>[1,1,1,1,1,0,0,0,0,0] [1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0] [1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0] [1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0] [1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,2,3,1,4]=>[1,1,1,1,1,0,0,0,0,0] [1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0] [1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0] [1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0] [1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0] [1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0] [1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0] [1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,1,2,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,1,2,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[6,1,2,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,1,2,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,1,3,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,1,3,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[6,1,3,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[6,1,3,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[6,1,3,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,1,4,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[6,1,4,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[6,1,5,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,2,1,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,2,1,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[6,2,1,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[6,2,3,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[6,2,3,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,2,3,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[6,2,4,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[6,2,5,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,2,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[6,5,2,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,4,5,7,6,1]=>[7,1,2,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,4,6,5,7,1]=>[7,1,2,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,4,7,5,6,1]=>[7,1,2,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,4,7,6,5,1]=>[7,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,5,4,6,7,1]=>[7,1,2,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,5,4,7,6,1]=>[7,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,6,4,5,7,1]=>[7,1,2,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,7,4,5,6,1]=>[7,1,2,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,7,4,6,5,1]=>[7,1,2,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,6,5,4,7,1]=>[7,1,2,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,7,5,4,6,1]=>[7,1,2,5,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,7,5,6,4,1]=>[7,1,2,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,3,7,6,5,4,1]=>[7,1,2,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,4,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,4,3,5,7,6,1]=>[7,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,4,3,6,5,7,1]=>[7,1,3,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,4,3,7,5,6,1]=>[7,1,3,2,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,4,3,7,6,5,1]=>[7,1,3,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,5,3,4,6,7,1]=>[7,1,3,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,5,3,4,7,6,1]=>[7,1,3,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,6,3,4,5,7,1]=>[7,1,3,4,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,3,4,5,6,1]=>[7,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,3,4,6,5,1]=>[7,1,3,4,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,6,3,5,4,7,1]=>[7,1,3,5,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,3,5,4,6,1]=>[7,1,3,5,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,3,5,6,4,1]=>[7,1,3,6,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,3,6,5,4,1]=>[7,1,3,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,5,4,3,6,7,1]=>[7,1,4,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,5,4,3,7,6,1]=>[7,1,4,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,6,4,3,5,7,1]=>[7,1,4,3,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,4,3,5,6,1]=>[7,1,4,3,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,4,3,6,5,1]=>[7,1,4,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,6,4,5,3,7,1]=>[7,1,5,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,4,5,3,6,1]=>[7,1,5,3,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,4,5,6,3,1]=>[7,1,6,3,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,4,6,5,3,1]=>[7,1,6,3,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,6,5,4,3,7,1]=>[7,1,5,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,5,4,3,6,1]=>[7,1,5,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,5,4,6,3,1]=>[7,1,6,4,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,6,4,5,3,1]=>[7,1,6,4,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[2,7,6,5,4,3,1]=>[7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,4,5,7,6,1]=>[7,2,1,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,4,6,5,7,1]=>[7,2,1,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,4,7,5,6,1]=>[7,2,1,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,4,7,6,5,1]=>[7,2,1,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,5,4,6,7,1]=>[7,2,1,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,5,4,7,6,1]=>[7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,6,4,5,7,1]=>[7,2,1,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,7,4,5,6,1]=>[7,2,1,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,7,4,6,5,1]=>[7,2,1,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,6,5,4,7,1]=>[7,2,1,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,7,5,4,6,1]=>[7,2,1,5,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,7,5,6,4,1]=>[7,2,1,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[3,2,7,6,5,4,1]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,2,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,2,3,5,7,6,1]=>[7,2,3,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,2,3,6,5,7,1]=>[7,2,3,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,2,3,7,5,6,1]=>[7,2,3,1,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,2,3,7,6,5,1]=>[7,2,3,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,2,3,4,6,7,1]=>[7,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,2,3,4,7,6,1]=>[7,2,3,4,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,2,3,4,5,7,1]=>[7,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,3,4,5,6,1]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,3,4,6,5,1]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,2,3,5,4,7,1]=>[7,2,3,5,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,3,5,4,6,1]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,3,5,6,4,1]=>[7,2,3,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,3,6,5,4,1]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,2,4,3,6,7,1]=>[7,2,4,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,2,4,3,7,6,1]=>[7,2,4,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,2,4,3,5,7,1]=>[7,2,4,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,4,3,5,6,1]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,4,3,6,5,1]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,2,4,5,3,7,1]=>[7,2,5,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,4,5,3,6,1]=>[7,2,5,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,4,5,6,3,1]=>[7,2,6,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,4,6,5,3,1]=>[7,2,6,3,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,2,5,4,3,7,1]=>[7,2,5,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,5,4,3,6,1]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,5,4,6,3,1]=>[7,2,6,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,6,4,5,3,1]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,3,2,5,7,6,1]=>[7,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,3,2,6,5,7,1]=>[7,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,3,2,7,5,6,1]=>[7,3,2,1,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[4,3,2,7,6,5,1]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,3,2,4,6,7,1]=>[7,3,2,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,3,2,4,7,6,1]=>[7,3,2,4,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,3,2,4,5,7,1]=>[7,3,2,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,2,4,5,6,1]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,2,4,6,5,1]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,3,2,5,4,7,1]=>[7,3,2,5,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,2,5,4,6,1]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,2,5,6,4,1]=>[7,3,2,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,3,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,3,4,2,7,6,1]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,3,4,2,5,7,1]=>[7,4,2,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,4,2,5,6,1]=>[7,4,2,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,4,2,6,5,1]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,3,4,5,2,7,1]=>[7,5,2,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,4,5,2,6,1]=>[7,5,2,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,4,5,6,2,1]=>[7,6,2,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,4,6,5,2,1]=>[7,6,2,3,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,5,4,2,6,1]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,5,4,6,2,1]=>[7,6,2,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,6,4,5,2,1]=>[7,6,2,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[5,4,3,2,7,6,1]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,4,3,2,5,7,1]=>[7,4,3,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,4,3,2,5,6,1]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,4,3,5,6,2,1]=>[7,6,3,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,4,3,6,5,2,1]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,5,3,4,6,2,1]=>[7,6,3,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,6,3,4,5,2,1]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [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]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,8,5,6,7,1]=>[8,1,2,3,5,6,7,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [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]=>[2,3,7,4,5,6,8,1]=>[8,1,2,4,5,6,3,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [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]=>[8,3,2,5,4,7,6,1]=>[8,3,2,5,4,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [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]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [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]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [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]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
inverse
Description
Sends a permutation to its inverse.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.