Identifier
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00237: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-3
[1,0]=>[1]=>[1]=>{{1}} [1,0,1,0]=>[1,2]=>[1,2]=>{{1},{2}} [1,1,0,0]=>[2,1]=>[2,1]=>{{1,2}} [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}} [1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>{{1},{2,3}} [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>{{1,2},{3}} [1,1,0,1,0,0]=>[2,3,1]=>[3,2,1]=>{{1,3},{2}} [1,1,1,0,0,0]=>[3,2,1]=>[2,3,1]=>{{1,2,3}} [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}} [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>{{1},{2},{3,4}} [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}} [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>{{1},{2,4},{3}} [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,3,4,2]=>{{1},{2,3,4}} [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}} [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>{{1,2},{3,4}} [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}} [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,2,3,1]=>{{1,4},{2},{3}} [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[3,2,4,1]=>{{1,3,4},{2}} [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[2,3,1,4]=>{{1,2,3},{4}} [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,3,2,1]=>{{1,4},{2,3}} [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[3,4,2,1]=>{{1,2,3,4}} [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[2,3,4,1]=>{{1,2,3,4}} [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}} [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}} [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}} [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}} [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}} [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}} [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}} [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}} [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}} [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}} [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}} [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}} [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[1,4,5,3,2]=>{{1},{2,3,4,5}} [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,3,4,5,2]=>{{1},{2,3,4,5}} [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}} [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}} [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}} [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}} [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,4,5,3]=>{{1,2},{3,4,5}} [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}} [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}} [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}} [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}} [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}} [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,4,3,1]=>{{1,5},{2},{3,4}} [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[4,2,5,3,1]=>{{1,3,4,5},{2}} [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[3,2,4,5,1]=>{{1,3,4,5},{2}} [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}} [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[2,3,1,5,4]=>{{1,2,3},{4,5}} [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}} [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}} [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[4,3,2,5,1]=>{{1,4,5},{2,3}} [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[3,4,2,1,5]=>{{1,2,3,4},{5}} [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,4,2,3,1]=>{{1,5},{2,3,4}} [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[4,5,2,3,1]=>{{1,2,3,4,5}} [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[3,4,5,1,2]=>{{1,2,3,4,5}} [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}} [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}} [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[4,3,5,2,1]=>{{1,2,3,4,5}} [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[2,4,5,3,1]=>{{1,2,3,4,5}} [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[1,6,5,3,4,2]=>{{1},{2,6},{3,4,5}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[1,5,6,3,4,2]=>{{1},{2,3,4,5,6}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[1,4,5,6,2,3]=>{{1},{2,3,4,5,6}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[2,1,5,6,4,3]=>{{1,2},{3,4,5,6}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[5,2,3,6,4,1]=>{{1,4,5,6},{2},{3}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[4,2,5,3,1,6]=>{{1,3,4,5},{2},{6}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[6,2,5,3,4,1]=>{{1,6},{2},{3,4,5}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[5,2,6,3,4,1]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[4,2,5,6,1,3]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[5,2,4,6,3,1]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[3,2,5,6,4,1]=>{{1,3,4,5,6},{2}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[5,3,2,6,4,1]=>{{1,4,5,6},{2,3}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[3,4,2,1,6,5]=>{{1,2,3,4},{5,6}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>{{1,2,3,4,5},{6}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[4,5,2,6,1,3]=>{{1,2,3,4,5,6}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[3,4,5,1,2,6]=>{{1,2,3,4,5},{6}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[5,6,4,2,3,1]=>{{1,2,3,4,5,6}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[3,5,6,2,1,4]=>{{1,2,3,4,5,6}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[3,4,5,6,2,1]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>{{1,6},{2,3,4,5}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[4,3,5,6,1,2]=>{{1,2,3,4,5,6}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>{{1,2,3,4,5},{6}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>{{1,2,3,4,5,6}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>{{1,2,3,4,5,6}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[2,4,5,6,1,3]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>{{1,2,3,4,5,6}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}} [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}} [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}} [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}} [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}} [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}} [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}} [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}} [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}} [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}} [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}} [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}} [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}} [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}} [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}} [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}} [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>[1,2,7,6,4,5,3]=>{{1},{2},{3,7},{4,5,6}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>[1,2,6,7,4,5,3]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>[1,2,5,6,7,3,4]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}} [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}} [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}} [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}} [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}} [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}} [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}} [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}} [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}} [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}} [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>{{1},{2,6},{3},{4,5},{7}} [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>[1,7,3,6,4,5,2]=>{{1},{2,7},{3},{4,5,6}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>[1,6,3,7,4,5,2]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>[1,5,3,6,7,2,4]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}} [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}} [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}} [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}} [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>{{1},{2,6},{3,4},{5},{7}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}} [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>[1,6,4,3,7,5,2]=>{{1},{2,5,6,7},{3,4}} [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}} [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}} [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>[1,6,5,3,4,2,7]=>{{1},{2,6},{3,4,5},{7}} [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>[1,7,5,3,4,6,2]=>{{1},{2,7},{3,4,5},{6}} [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>[1,6,5,3,4,7,2]=>{{1},{2,6,7},{3,4,5}} [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>[1,5,6,3,4,2,7]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>[1,7,6,3,4,5,2]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>[1,6,7,3,4,5,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>[1,5,6,3,7,2,4]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>[1,4,5,6,2,3,7]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>[1,7,6,5,3,4,2]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>[1,6,7,5,3,4,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>[1,4,6,7,3,2,5]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}} [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>{{1},{2,6},{3,4,5},{7}} [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}} [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}} [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>[1,7,4,6,3,5,2]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>[1,6,4,7,3,5,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>[1,5,4,6,7,2,3]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>[1,7,5,6,4,3,2]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>[1,3,6,7,4,5,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>[1,3,5,6,7,2,4]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}} [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}} [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}} [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}} [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}} [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}} [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}} [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}} [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}} [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}} [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}} [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>[2,1,3,6,7,5,4]=>{{1,2},{3},{4,5,6,7}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}} [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}} [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}} [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}} [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>{{1,2},{3,6},{4},{5},{7}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}} [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}} [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}} [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>[2,1,6,4,7,5,3]=>{{1,2},{3,5,6,7},{4}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}} [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}} [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}} [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}} [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>[2,1,5,6,4,3,7]=>{{1,2},{3,4,5,6},{7}} [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>[2,1,7,6,4,5,3]=>{{1,2},{3,7},{4,5,6}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>[2,1,6,7,4,5,3]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>[2,1,5,6,7,3,4]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}} [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>[2,1,6,5,7,4,3]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>[2,1,4,6,7,5,3]=>{{1,2},{3,4,5,6,7}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}} [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}} [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}} [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}} [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>[3,2,1,6,7,5,4]=>{{1,3},{2},{4,5,6,7}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}} [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}} [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}} [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>{{1,4},{2},{3},{5,6},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>{{1,4},{2},{3},{5,7},{6}} [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>{{1,4},{2},{3},{5,6,7}} [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}} [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}} [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}} [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}} [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[6,2,3,4,7,5,1]=>{{1,5,6,7},{2},{3},{4}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}} [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>{{1,4,5},{2},{3},{6,7}} [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>{{1,6},{2},{3},{4,5},{7}} [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>{{1,7},{2},{3},{4,5},{6}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}} [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>[5,2,3,6,4,1,7]=>{{1,4,5,6},{2},{3},{7}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>[7,2,3,6,4,5,1]=>{{1,7},{2},{3},{4,5,6}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[6,2,3,7,4,5,1]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[5,2,3,6,7,1,4]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}} [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>[6,2,3,5,7,4,1]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>[4,2,3,6,7,5,1]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}} [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>{{1,5},{2},{3,4},{6},{7}} [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>{{1,5},{2},{3,4},{6,7}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>{{1,6},{2},{3,4},{5},{7}} [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>{{1,7},{2},{3,4},{5},{6}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}} [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>{{1,5,6},{2},{3,4},{7}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>[6,2,4,3,7,5,1]=>{{1,5,6,7},{2},{3,4}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}} [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>[4,2,5,3,1,6,7]=>{{1,3,4,5},{2},{6},{7}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>[4,2,5,3,1,7,6]=>{{1,3,4,5},{2},{6,7}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>[6,2,5,3,4,1,7]=>{{1,6},{2},{3,4,5},{7}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>[7,2,5,3,4,6,1]=>{{1,7},{2},{3,4,5},{6}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>[6,2,5,3,4,7,1]=>{{1,6,7},{2},{3,4,5}} [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>[5,2,6,3,4,1,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>[7,2,6,3,4,5,1]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[6,2,7,3,4,5,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>[5,2,6,3,7,1,4]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>[4,2,5,6,1,3,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[7,2,6,5,3,4,1]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>[6,2,7,5,3,4,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>[4,2,6,7,3,1,5]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>[4,2,5,6,7,3,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}} [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}} [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>{{1,6},{2},{3,4,5},{7}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>[5,2,4,6,3,1,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>[7,2,4,6,3,5,1]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>[6,2,4,7,3,5,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>[5,2,4,6,7,1,3]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>[3,2,5,6,4,1,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>[7,2,5,6,4,3,1]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>[6,2,5,7,4,3,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>[3,2,6,7,4,5,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>[3,2,5,6,7,1,4]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}} [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}} [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>[6,2,4,5,7,3,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>[3,2,6,5,7,4,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>[3,2,5,6,4,7,1]=>{{1,3,4,5,6,7},{2}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}} [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}} [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}} [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}} [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}} [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}} [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}} [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}} [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>[2,3,1,6,7,5,4]=>{{1,2,3},{4,5,6,7}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}} [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}} [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}} [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}} [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>{{1,5},{2,3},{4},{6,7}} [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}} [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}} [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}} [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}} [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>[6,3,2,4,7,5,1]=>{{1,5,6,7},{2,3},{4}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}} [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}} [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}} [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>{{1,6},{2,3},{4,5},{7}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}} [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>[5,3,2,6,4,1,7]=>{{1,4,5,6},{2,3},{7}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>[7,3,2,6,4,5,1]=>{{1,7},{2,3},{4,5,6}} [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>[6,3,2,7,4,5,1]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>[5,3,2,6,7,1,4]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}} [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}} [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>[6,3,2,5,7,4,1]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>[4,3,2,6,7,5,1]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>[3,4,2,1,5,7,6]=>{{1,2,3,4},{5},{6,7}} [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>[3,4,2,1,6,5,7]=>{{1,2,3,4},{5,6},{7}} [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>[3,4,2,1,7,6,5]=>{{1,2,3,4},{5,7},{6}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>[3,4,2,1,6,7,5]=>{{1,2,3,4},{5,6,7}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>[5,4,2,3,1,7,6]=>{{1,5},{2,3,4},{6,7}} [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>{{1,6},{2,3,4},{5},{7}} [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>[6,4,2,3,5,7,1]=>{{1,6,7},{2,3,4},{5}} [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>[5,4,2,3,6,1,7]=>{{1,5,6},{2,3,4},{7}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>[7,4,2,3,6,5,1]=>{{1,7},{2,3,4},{5,6}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>[6,4,2,3,7,5,1]=>{{1,5,6,7},{2,3,4}} [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}} [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>[4,5,2,3,1,7,6]=>{{1,2,3,4,5},{6,7}} [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>[5,6,2,3,7,1,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>[4,5,2,6,1,3,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>[7,6,2,5,3,4,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>[6,7,2,5,3,4,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>[4,6,2,7,3,1,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>[4,5,2,6,7,3,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>[3,4,5,1,2,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>[3,4,5,1,2,7,6]=>{{1,2,3,4,5},{6,7}} [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>[6,5,4,2,3,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>[6,5,4,2,3,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>[5,6,4,2,3,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>[6,7,4,2,3,5,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>[5,6,4,2,7,1,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>[3,5,6,2,1,4,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>[7,6,5,2,4,3,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>[3,6,7,2,4,1,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>[3,5,6,2,7,4,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>[3,4,5,6,2,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>[7,6,4,5,2,3,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>[6,7,4,5,2,3,1]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>[3,6,7,5,2,1,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>[3,5,7,6,4,1,2]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>[3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}} [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}} [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}} [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>{{1,5},{2,3,4},{6,7}} [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}} [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}} [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}} [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>[6,3,4,2,7,5,1]=>{{1,5,6,7},{2,3,4}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}} [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>[4,3,5,2,1,7,6]=>{{1,2,3,4,5},{6,7}} [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>[6,3,5,2,4,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>[5,3,6,2,7,1,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>[4,3,5,6,1,2,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>[7,3,6,5,2,4,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>[6,3,7,5,2,4,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>[4,3,6,7,2,1,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>[2,4,5,3,1,7,6]=>{{1,2,3,4,5},{6,7}} [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>[6,4,5,3,2,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>[5,4,6,3,7,1,2]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>[2,5,6,3,7,1,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>[2,4,5,6,1,3,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>[7,4,5,6,2,3,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>[6,4,5,7,2,3,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>[2,6,7,5,3,4,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>[2,5,7,6,4,3,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>[2,4,5,6,7,3,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}} [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}} [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>[5,3,4,6,7,1,2]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>[2,5,4,6,7,1,3]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>[2,4,5,6,1,7,3]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}} [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}} [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>{{1},{2,4},{3},{5,7},{6},{8}} [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}} [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>{{1,2},{3},{4},{5},{6},{7,8}} [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}} [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>{{1,3},{2},{4},{5},{6,8},{7}} [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}} [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>{{1,2,3},{4},{5},{6,7,8}} [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,2,3,1,8,6,7,5]=>[3,4,2,1,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
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
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
This map is similar to Mp00235descent views to invisible inversion bottoms, but different beginning with permutations of six elements.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].