Identifier
Mp00085: Standard tableaux Schützenberger involutionStandard tableaux
Mp00081: Standard tableaux reading word permutationPermutations
Mp00160: Permutations graph of inversions Graphs
Images
=>
Cc0007;cc-rep-0Cc0007;cc-rep-1Cc0020;cc-rep-3
[[1]]=>[[1]]=>[1]=>([],1) [[1,2]]=>[[1,2]]=>[1,2]=>([],2) [[1],[2]]=>[[1],[2]]=>[2,1]=>([(0,1)],2) [[1,2,3]]=>[[1,2,3]]=>[1,2,3]=>([],3) [[1,3],[2]]=>[[1,2],[3]]=>[3,1,2]=>([(0,2),(1,2)],3) [[1,2],[3]]=>[[1,3],[2]]=>[2,1,3]=>([(1,2)],3) [[1],[2],[3]]=>[[1],[2],[3]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3) [[1,2,3,4]]=>[[1,2,3,4]]=>[1,2,3,4]=>([],4) [[1,3,4],[2]]=>[[1,2,3],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4) [[1,2,4],[3]]=>[[1,2,4],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4) [[1,2,3],[4]]=>[[1,3,4],[2]]=>[2,1,3,4]=>([(2,3)],4) [[1,3],[2,4]]=>[[1,3],[2,4]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4) [[1,2],[3,4]]=>[[1,2],[3,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4) [[1,4],[2],[3]]=>[[1,2],[3],[4]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4) [[1,3],[2],[4]]=>[[1,3],[2],[4]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4) [[1,2],[3],[4]]=>[[1,4],[2],[3]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4) [[1],[2],[3],[4]]=>[[1],[2],[3],[4]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(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]]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5) [[1,2,4,5],[3]]=>[[1,2,3,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5) [[1,2,3,5],[4]]=>[[1,2,4,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5) [[1,2,3,4],[5]]=>[[1,3,4,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5) [[1,3,5],[2,4]]=>[[1,2,4],[3,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5) [[1,2,5],[3,4]]=>[[1,2,3],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) [[1,3,4],[2,5]]=>[[1,3,4],[2,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5) [[1,2,4],[3,5]]=>[[1,3,5],[2,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5) [[1,2,3],[4,5]]=>[[1,2,5],[3,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5) [[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,2,5],[3],[4]]=>[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,3,4],[2],[5]]=>[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [[1,2,4],[3],[5]]=>[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5) [[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5) [[1,4],[2,5],[3]]=>[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) [[1,3],[2,5],[4]]=>[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) [[1,2],[3,5],[4]]=>[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) [[1,3],[2,4],[5]]=>[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5) [[1,2],[3,4],[5]]=>[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) [[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,4],[2],[3],[5]]=>[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,3],[2],[4],[5]]=>[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [[1],[2],[3],[4],[5]]=>[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(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]]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6) [[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6) [[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6) [[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6) [[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) [[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6) [[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6) [[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6) [[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,5,6],[2],[4]]=>[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,4,6],[3],[5]]=>[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,4,5],[2],[6]]=>[[1,3,4,5],[2],[6]]=>[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]]=>[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6) [[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [[1,2,4],[3,5,6]]=>[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) [[1,4,6],[2,5],[3]]=>[[1,2,4],[3,5],[6]]=>[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) [[1,3,6],[2,5],[4]]=>[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) [[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,6],[2,4],[5]]=>[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [[1,2,6],[3,4],[5]]=>[[1,2,4],[3,6],[5]]=>[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) [[1,4,5],[2,6],[3]]=>[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,5],[2,6],[4]]=>[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,5],[3,6],[4]]=>[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,4],[2,6],[5]]=>[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) [[1,2,4],[3,6],[5]]=>[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) [[1,2,3],[4,6],[5]]=>[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,3,5],[2,4],[6]]=>[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) [[1,2,5],[3,4],[6]]=>[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) [[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) [[1,2,4],[3,5],[6]]=>[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6) [[1,2,3],[4,5],[6]]=>[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) [[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,6],[2],[4],[5]]=>[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,6],[3],[4],[5]]=>[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,5],[2],[4],[6]]=>[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3,4],[2],[5],[6]]=>[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,4],[3],[5],[6]]=>[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,4],[2,5],[3,6]]=>[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3],[2,5],[4,6]]=>[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2],[3,5],[4,6]]=>[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,3],[2,4],[5,6]]=>[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,2],[3,4],[5,6]]=>[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [[1,5],[2,6],[3],[4]]=>[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,4],[2,6],[3],[5]]=>[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3],[2,6],[4],[5]]=>[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) [[1,2],[3,6],[4],[5]]=>[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,4],[2,5],[3],[6]]=>[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3],[2,5],[4],[6]]=>[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2],[3,5],[4],[6]]=>[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) [[1,3],[2,4],[5],[6]]=>[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2],[3,4],[5],[6]]=>[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,5],[2],[3],[4],[6]]=>[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,4],[2],[3],[5],[6]]=>[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,3],[2],[4],[5],[6]]=>[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [[1],[2],[3],[4],[5],[6]]=>[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(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]]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) [[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7) [[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7) [[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7) [[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>([(5,6)],7) [[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]=>[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) [[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]=>[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]]=>[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7) [[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>([(3,6),(4,5),(5,6)],7) [[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7) [[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[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) [[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5,6,7],[3],[4]]=>[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]=>[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) [[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,5,7],[3],[6]]=>[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]=>[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]]=>[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>([(4,5),(4,6),(5,6)],7) [[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]=>[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) [[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [[1,4,6,7],[2,5],[3]]=>[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7) [[1,3,6,7],[2,4],[5]]=>[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7) [[1,2,6,7],[3,4],[5]]=>[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7) [[1,4,5,7],[2,6],[3]]=>[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,7],[2,6],[4]]=>[[1,2,4,6],[3,5],[7]]=>[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) [[1,2,5,7],[3,6],[4]]=>[[1,2,4,7],[3,5],[6]]=>[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) [[1,3,4,7],[2,6],[5]]=>[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,4,7],[3,6],[5]]=>[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,3,7],[4,6],[5]]=>[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,7],[2,4],[6]]=>[[1,2,4,6],[3,7],[5]]=>[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) [[1,2,5,7],[3,4],[6]]=>[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4,7],[2,5],[6]]=>[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,4,7],[3,5],[6]]=>[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,3,7],[4,5],[6]]=>[[1,2,4,7],[3,6],[5]]=>[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) [[1,4,5,6],[2,7],[3]]=>[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,6],[2,7],[4]]=>[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,6],[2,7],[5]]=>[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,6],[3,7],[5]]=>[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,5],[2,7],[6]]=>[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,4,5],[3,7],[6]]=>[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,3,5],[4,7],[6]]=>[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,3,4],[5,7],[6]]=>[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,5,6],[2,4],[7]]=>[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) [[1,2,5,6],[3,4],[7]]=>[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7) [[1,3,4,6],[2,5],[7]]=>[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) [[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3,6],[4,5],[7]]=>[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) [[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) [[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>([(2,5),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,3,4],[5,6],[7]]=>[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) [[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>([(0,5),(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) [[1,3,6,7],[2],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>([(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) [[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>([(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) [[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>([(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) [[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5,7],[3],[4],[6]]=>[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,7],[2],[5],[6]]=>[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5,6],[2],[4],[7]]=>[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5,6],[3],[4],[7]]=>[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,6],[2],[5],[7]]=>[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]=>[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) [[1,2,4,5],[3],[6],[7]]=>[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,6],[2,5,7],[3]]=>[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6],[2,5,7],[4]]=>[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>([(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) [[1,2,6],[3,5,7],[4]]=>[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>([(0,5),(0,6),(1,2),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6],[2,4,7],[5]]=>[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>([(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,6],[3,4,7],[5]]=>[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) [[1,4,5],[2,6,7],[3]]=>[[1,2,5],[3,4,6],[7]]=>[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) [[1,3,5],[2,6,7],[4]]=>[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,5],[3,6,7],[4]]=>[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4],[2,6,7],[5]]=>[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7) [[1,2,4],[3,6,7],[5]]=>[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7) [[1,2,3],[4,6,7],[5]]=>[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>([(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)],7) [[1,3,5],[2,4,7],[6]]=>[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,5],[3,4,7],[6]]=>[[1,2,5],[3,4,7],[6]]=>[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) [[1,3,4],[2,5,7],[6]]=>[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4],[3,5,7],[6]]=>[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3],[4,5,7],[6]]=>[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,3,5],[2,4,6],[7]]=>[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7) [[1,2,5],[3,4,6],[7]]=>[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,3,4],[2,5,6],[7]]=>[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,4],[3,5,6],[7]]=>[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>([(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [[1,2,3],[4,5,6],[7]]=>[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7) [[1,4,7],[2,5],[3,6]]=>[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,7],[2,5],[4,6]]=>[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7) [[1,2,7],[3,5],[4,6]]=>[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,3,7],[2,4],[5,6]]=>[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,7],[3,4],[5,6]]=>[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,4,6],[2,5],[3,7]]=>[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6],[2,5],[4,7]]=>[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>([(0,3),(0,4),(0,6),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7) [[1,2,6],[3,5],[4,7]]=>[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,3,6],[2,4],[5,7]]=>[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>([(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) [[1,2,6],[3,4],[5,7]]=>[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>([(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) [[1,4,5],[2,6],[3,7]]=>[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,6],[4,7]]=>[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5],[3,6],[4,7]]=>[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4],[2,6],[5,7]]=>[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>([(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4],[3,6],[5,7]]=>[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3],[4,6],[5,7]]=>[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>([(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],[2,4],[6,7]]=>[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,5],[3,4],[6,7]]=>[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4],[2,5],[6,7]]=>[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>([(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,4],[3,5],[6,7]]=>[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,3],[4,5],[6,7]]=>[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,5,7],[2,6],[3],[4]]=>[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(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]]=>[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(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) [[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>([(0,1),(0,2),(0,3),(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) [[1,4,7],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>([(0,5),(0,6),(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) [[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2,7],[3,5],[4],[6]]=>[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>([(0,1),(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,7],[2,4],[5],[6]]=>[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,7],[3,4],[5],[6]]=>[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,5,6],[2,7],[3],[4]]=>[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>([(0,4),(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),(5,6)],7) [[1,4,6],[2,7],[3],[5]]=>[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>([(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),(5,6)],7) [[1,3,6],[2,7],[4],[5]]=>[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,6],[3,7],[4],[5]]=>[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,5],[2,7],[3],[6]]=>[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,7],[4],[6]]=>[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5],[3,7],[4],[6]]=>[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>([(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) [[1,2,4],[3,7],[5],[6]]=>[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>([(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) [[1,2,3],[4,7],[5],[6]]=>[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,4,6],[2,5],[3],[7]]=>[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,3,6],[2,5],[4],[7]]=>[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>([(0,3),(0,5),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,6],[3,5],[4],[7]]=>[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>([(0,2),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6],[2,4],[5],[7]]=>[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>([(0,3),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,6],[3,4],[5],[7]]=>[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>([(0,3),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7) [[1,4,5],[2,6],[3],[7]]=>[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,6],[4],[7]]=>[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5],[3,6],[4],[7]]=>[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4],[2,6],[5],[7]]=>[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>([(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],[3,6],[5],[7]]=>[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3],[4,6],[5],[7]]=>[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) [[1,3,5],[2,4],[6],[7]]=>[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>([(0,4),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) [[1,2,5],[3,4],[6],[7]]=>[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) [[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3],[4,5],[6],[7]]=>[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>([(0,3),(0,4),(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),(5,6)],7) [[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>([(0,4),(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),(5,6)],7) [[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>([(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),(5,6)],7) [[1,3,7],[2],[4],[5],[6]]=>[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>([(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),(5,6)],7) [[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>([(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),(5,6)],7) [[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>([(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),(4,5),(4,6),(5,6)],7) [[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,6],[2],[4],[5],[7]]=>[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>([(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),(5,6)],7) [[1,3,5],[2],[4],[6],[7]]=>[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3,4],[2],[5],[6],[7]]=>[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,5],[2,6],[3,7],[4]]=>[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4],[2,6],[3,7],[5]]=>[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,6],[4,7],[5]]=>[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(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) [[1,2],[3,6],[4,7],[5]]=>[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>([(0,2),(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4],[2,5],[3,7],[6]]=>[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(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],[2,5],[4,7],[6]]=>[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) [[1,2],[3,5],[4,7],[6]]=>[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3],[2,4],[5,7],[6]]=>[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>([(0,3),(0,5),(0,6),(1,2),(1,4),(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],[5,7],[6]]=>[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,4],[2,5],[3,6],[7]]=>[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,5],[4,6],[7]]=>[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>([(0,1),(0,4),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2],[3,5],[4,6],[7]]=>[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,4],[5,6],[7]]=>[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) [[1,2],[3,4],[5,6],[7]]=>[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,6],[2,7],[3],[4],[5]]=>[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(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]]=>[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(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) [[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(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) [[1,2],[3,7],[4],[5],[6]]=>[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>([(0,5),(0,6),(1,2),(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) [[1,5],[2,6],[3],[4],[7]]=>[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>([(0,3),(0,5),(0,6),(1,2),(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) [[1,4],[2,6],[3],[5],[7]]=>[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,6],[4],[5],[7]]=>[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2],[3,6],[4],[5],[7]]=>[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,4],[2,5],[3],[6],[7]]=>[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,3],[2,5],[4],[6],[7]]=>[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2],[3,5],[4],[6],[7]]=>[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>([(0,1),(0,6),(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) [[1,3],[2,4],[5],[6],[7]]=>[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,2],[3,4],[5],[6],[7]]=>[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(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),(5,6)],7) [[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(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),(5,6)],7) [[1,5],[2],[3],[4],[6],[7]]=>[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>([(0,4),(0,5),(0,6),(1,2),(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),(5,6)],7) [[1,4],[2],[3],[5],[6],[7]]=>[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>([(0,5),(0,6),(1,2),(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),(5,6)],7) [[1,3],[2],[4],[5],[6],[7]]=>[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>([(0,6),(1,2),(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),(5,6)],7) [[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>([(1,2),(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),(5,6)],7) [[1],[2],[3],[4],[5],[6],[7]]=>[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(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),(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) [[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) [[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) [[1,2,7,8],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) [[1,2,3],[4,5,6],[7],[8]]=>[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>([(0,2),(0,3),(0,7),(1,2),(1,3),(1,7),(2,6),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [[1,2],[3,4],[5,6],[7,8]]=>[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) [[1,2],[3,4],[5],[6],[7],[8]]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.
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
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.