Identifier
Mp00081: Standard tableaux reading word permutationPermutations
Mp00235: Permutations descent views to invisible inversion bottomsPermutations
Mp00160: Permutations graph of inversions Graphs
Images
=>
Cc0007;cc-rep-0Cc0020;cc-rep-3
[[1]]=>[1]=>[1]=>([],1) [[1,2]]=>[1,2]=>[1,2]=>([],2) [[1],[2]]=>[2,1]=>[2,1]=>([(0,1)],2) [[1,2,3]]=>[1,2,3]=>[1,2,3]=>([],3) [[1,3],[2]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3) [[1,2],[3]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3) [[1],[2],[3]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3) [[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4) [[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4) [[1,2,4],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4) [[1,2,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4) [[1,3],[2,4]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4) [[1,2],[3,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4) [[1,4],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4) [[1,3],[2],[4]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4) [[1,2],[3],[4]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4) [[1],[2],[3],[4]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4) [[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5) [[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5) [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5) [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5) [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5) [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5) [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5) [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5) [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5) [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5) [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5) [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5) [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5) [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5) [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5) [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5) [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5) [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5) [[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6) [[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6) [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6) [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6) [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6) [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6) [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6) [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6) [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6) [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6) [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6) [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6) [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6) [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>([(1,5),(2,4),(3,4),(3,5)],6) [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>([(1,5),(2,5),(3,4),(4,5)],6) [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>([(1,5),(2,5),(3,5),(4,5)],6) [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7) [[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7) [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7) [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7) [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7) [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>([(4,6),(5,6)],7) [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>([(3,6),(4,5),(5,6)],7) [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>([(3,6),(4,5),(5,6)],7) [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7) [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>([(2,6),(3,5),(4,5),(4,6)],7) [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7) [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[5,4,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[6,4,1,2,3,5,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[6,1,4,3,2,5,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[6,5,1,3,2,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[6,1,5,2,3,4,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[4,6,1,2,3,5,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[5,6,1,3,2,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[5,1,6,2,3,4,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[7,4,1,2,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[7,1,4,3,2,5,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[7,5,1,3,2,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[7,1,5,2,3,4,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[7,1,2,5,4,3,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[7,6,1,3,4,2,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[7,1,6,2,4,3,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[4,7,1,2,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[5,7,1,3,2,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[5,1,7,2,3,4,6]=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[6,7,1,3,4,2,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[6,1,7,2,4,3,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[6,1,2,7,3,4,5]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>([(3,6),(4,6),(5,6)],7) [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7) [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>([(2,6),(3,5),(4,5),(4,6)],7) [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7) [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7) [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7) [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7) [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7) [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[7,3,2,1,5,4,6]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[7,4,1,2,5,3,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[7,1,4,3,5,2,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[7,5,1,2,4,3,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[7,1,5,3,4,2,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[7,3,2,1,4,6,5]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[7,4,1,2,3,6,5]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[7,1,4,3,2,6,5]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[7,5,1,3,2,6,4]=>([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[7,1,5,2,3,6,4]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[7,6,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[7,1,6,3,2,4,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[7,6,1,3,2,5,4]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[7,1,6,2,3,5,4]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[6,1,7,3,2,4,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[6,7,1,3,2,5,4]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[6,1,7,2,3,5,4]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[5,6,3,1,2,4,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[5,6,1,4,2,3,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[5,1,6,4,3,2,7]=>([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[4,6,1,2,5,3,7]=>([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[5,7,3,1,2,4,6]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[5,7,1,4,2,3,6]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[5,1,7,4,3,2,6]=>([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[4,7,1,2,5,3,6]=>([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[4,1,7,3,5,2,6]=>([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[6,7,3,1,4,2,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[6,7,1,4,3,2,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[6,1,7,4,2,3,5]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[6,7,1,3,5,2,4]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[6,1,7,2,5,3,4]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[6,1,2,7,5,4,3]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[4,7,1,2,3,6,5]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[5,7,1,3,2,6,4]=>([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[5,1,7,2,3,6,4]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[6,3,4,2,1,5,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[6,3,5,1,2,4,7]=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[6,4,1,5,2,3,7]=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[5,3,6,1,2,4,7]=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[5,4,1,6,2,3,7]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[4,5,1,2,6,3,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[7,3,4,2,1,5,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[7,3,5,1,2,4,6]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[7,4,1,5,2,3,6]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[7,1,4,5,3,2,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[7,3,6,1,4,2,5]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[7,4,1,6,3,2,5]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[7,1,4,6,2,3,5]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[7,5,1,3,6,2,4]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[7,1,5,2,6,3,4]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[5,3,7,1,2,4,6]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[5,4,1,7,2,3,6]=>([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7) [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[4,5,1,2,7,3,6]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[6,3,7,1,4,2,5]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[6,4,1,7,3,2,5]=>([(0,5),(0,6),(1,2),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[6,1,4,7,2,3,5]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[6,5,1,3,7,2,4]=>([(0,5),(0,6),(1,2),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[6,1,5,2,7,3,4]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[4,6,1,2,3,7,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[5,6,1,3,2,7,4]=>([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[5,1,6,2,3,7,4]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7) [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[6,7,4,3,1,2,5]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[6,7,5,1,3,2,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[6,7,1,5,4,2,3]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[6,1,7,5,4,3,2]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[5,7,6,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7) [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[5,7,1,6,2,4,3]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7) [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[5,1,7,6,3,4,2]=>([(0,5),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[4,7,1,2,6,5,3]=>([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[5,6,1,7,2,4,3]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[5,1,6,7,3,4,2]=>([(0,5),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[4,6,1,2,7,5,3]=>([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[7,3,4,5,2,1,6]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[7,3,4,6,1,2,5]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[7,3,5,1,6,2,4]=>([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[7,4,1,5,6,2,3]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[6,3,4,7,1,2,5]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[6,3,5,1,7,2,4]=>([(0,3),(0,5),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[6,4,1,5,7,2,3]=>([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[5,3,6,1,2,7,4]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7) [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[5,4,1,6,2,7,3]=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[4,5,1,2,6,7,3]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) [[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
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.
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
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.