Identifier
Mp00081: Standard tableaux reading word permutationPermutations
Mp00086: Permutations first fundamental transformationPermutations
Mp00065: Permutations permutation poset Posets
Images
=>
Cc0007;cc-rep-0Cc0014;cc-rep-3
[[1]]=>[1]=>[1]=>([],1) [[1,2]]=>[1,2]=>[1,2]=>([(0,1)],2) [[1],[2]]=>[2,1]=>[2,1]=>([],2) [[1,2,3]]=>[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3) [[1,3],[2]]=>[2,1,3]=>[2,1,3]=>([(0,2),(1,2)],3) [[1,2],[3]]=>[3,1,2]=>[2,3,1]=>([(1,2)],3) [[1],[2],[3]]=>[3,2,1]=>[3,1,2]=>([(1,2)],3) [[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4) [[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4) [[1,2,4],[3]]=>[3,1,2,4]=>[2,3,1,4]=>([(0,3),(1,2),(2,3)],4) [[1,2,3],[4]]=>[4,1,2,3]=>[2,3,4,1]=>([(1,2),(2,3)],4) [[1,3],[2,4]]=>[2,4,1,3]=>[3,2,4,1]=>([(1,3),(2,3)],4) [[1,2],[3,4]]=>[3,4,1,2]=>[2,4,3,1]=>([(1,2),(1,3)],4) [[1,4],[2],[3]]=>[3,2,1,4]=>[3,1,2,4]=>([(0,3),(1,2),(2,3)],4) [[1,3],[2],[4]]=>[4,2,1,3]=>[3,1,4,2]=>([(0,3),(1,2),(1,3)],4) [[1,2],[3],[4]]=>[4,3,1,2]=>[2,4,1,3]=>([(0,3),(1,2),(1,3)],4) [[1],[2],[3],[4]]=>[4,3,2,1]=>[4,1,2,3]=>([(1,2),(2,3)],4) [[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5) [[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5) [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[2,3,1,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5) [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5) [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5) [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[3,2,4,1,5]=>([(0,4),(1,3),(2,3),(3,4)],5) [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[2,4,3,1,5]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5) [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[3,2,4,5,1]=>([(1,4),(2,4),(4,3)],5) [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[2,4,3,5,1]=>([(1,2),(1,3),(2,4),(3,4)],5) [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[2,3,5,4,1]=>([(1,4),(4,2),(4,3)],5) [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[3,1,2,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5) [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[3,1,4,2,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5) [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[2,4,1,3,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5) [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[3,1,4,5,2]=>([(0,4),(1,2),(1,4),(4,3)],5) [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[2,4,1,5,3]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5) [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[2,3,5,1,4]=>([(0,4),(1,2),(2,3),(2,4)],5) [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,3,2,5,1]=>([(1,4),(2,4),(3,4)],5) [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[3,4,5,2,1]=>([(2,3),(3,4)],5) [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[2,5,4,3,1]=>([(1,2),(1,3),(1,4)],5) [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[3,4,5,1,2]=>([(0,3),(1,4),(4,2)],5) [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[2,5,4,1,3]=>([(0,4),(1,2),(1,3),(1,4)],5) [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[4,1,2,3,5]=>([(0,4),(1,2),(2,3),(3,4)],5) [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[4,1,2,5,3]=>([(0,4),(1,2),(2,3),(2,4)],5) [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[3,1,5,2,4]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5) [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[2,5,1,3,4]=>([(0,4),(1,2),(1,4),(4,3)],5) [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5) [[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6) [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6) [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6) [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6) [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6) [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6) [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6) [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>([(1,5),(2,5),(3,4),(5,3)],6) [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>([(1,2),(1,3),(2,5),(3,5),(5,4)],6) [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>([(1,4),(2,5),(3,5),(4,2),(4,3)],6) [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>([(1,4),(4,5),(5,2),(5,3)],6) [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6) [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[2,4,1,3,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[3,1,4,5,2,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[2,4,1,5,3,6]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[2,3,5,1,4,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[3,1,4,5,6,2]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6) [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[2,4,1,5,6,3]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[2,3,5,1,6,4]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6) [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>([(1,3),(1,4),(2,5),(3,5),(4,2)],6) [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>([(1,5),(2,5),(5,3),(5,4)],6) [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>([(1,5),(4,3),(5,2),(5,4)],6) [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[4,3,2,5,1,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6) [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[3,4,5,2,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[2,5,4,3,1,6]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[3,4,5,1,2,6]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6) [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[2,5,4,1,3,6]=>([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[4,3,2,5,6,1]=>([(1,5),(2,5),(3,5),(5,4)],6) [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[3,4,5,2,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6) [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[2,5,4,3,6,1]=>([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[3,5,4,6,2,1]=>([(2,3),(2,4),(3,5),(4,5)],6) [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[2,4,5,6,3,1]=>([(1,3),(1,5),(4,2),(5,4)],6) [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>([(1,5),(5,2),(5,3),(5,4)],6) [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[3,4,5,1,6,2]=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6) [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[2,5,4,1,6,3]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[3,5,4,6,1,2]=>([(0,4),(1,2),(1,3),(2,5),(3,5)],6) [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[2,4,5,6,1,3]=>([(0,5),(1,4),(1,5),(3,2),(4,3)],6) [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>([(0,5),(1,4),(4,2),(4,3),(4,5)],6) [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6) [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[4,1,2,5,3,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[3,1,5,2,4,6]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[2,5,1,3,4,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[4,1,2,5,6,3]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6) [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[3,1,5,2,6,4]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6) [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[4,5,3,6,1,2]=>([(0,5),(1,3),(2,4),(4,5)],6) [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,5,6,4,1,2]=>([(0,4),(1,3),(1,5),(5,2)],6) [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[2,6,5,4,1,3]=>([(0,5),(1,2),(1,3),(1,4),(1,5)],6) [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[3,4,6,1,5,2]=>([(0,4),(1,3),(1,5),(4,2),(4,5)],6) [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[5,4,2,3,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6) [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[4,5,2,6,3,1]=>([(1,4),(2,3),(2,5),(4,5)],6) [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[3,5,6,2,4,1]=>([(1,5),(2,3),(2,5),(3,4)],6) [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>([(1,3),(1,4),(1,5),(5,2)],6) [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[4,5,2,6,1,3]=>([(0,4),(1,4),(1,5),(2,3),(3,5)],6) [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[3,5,6,2,1,4]=>([(0,5),(1,5),(2,3),(2,5),(3,4)],6) [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>([(0,5),(1,2),(1,3),(1,4),(4,5)],6) [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[3,4,6,1,2,5]=>([(0,3),(1,4),(3,5),(4,2),(4,5)],6) [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6) [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6) [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[2,6,1,3,4,5]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6) [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6) [[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7) [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7) [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7) [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7) [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7) [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7) [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>([(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7) [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7) [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>([(1,5),(4,6),(5,4),(6,2),(6,3)],7) [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[2,4,1,3,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[3,1,4,5,2,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[2,4,1,5,3,6,7]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[2,3,5,1,4,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[3,1,4,5,6,2,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[2,4,1,5,6,3,7]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[2,3,5,1,6,4,7]=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[2,3,4,6,1,5,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[2,4,1,5,6,7,3]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[2,3,5,1,6,7,4]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[2,3,4,6,1,7,5]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[2,3,4,5,7,1,6]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7) [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>([(0,6),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>([(1,6),(2,6),(3,4),(3,5),(6,3)],7) [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7) [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[4,3,2,5,1,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[3,4,5,2,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[2,5,4,3,1,6,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[3,4,5,1,2,6,7]=>([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[2,5,4,1,3,6,7]=>([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[4,3,2,5,6,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[3,4,5,2,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[2,5,4,3,6,1,7]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[3,5,4,6,2,1,7]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[2,4,5,6,3,1,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7) [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[2,3,6,5,4,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[3,4,5,1,6,2,7]=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[2,5,4,1,6,3,7]=>([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[3,5,4,6,1,2,7]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,6),(5,6)],7) [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[2,4,5,6,1,3,7]=>([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7) [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[2,3,6,5,1,4,7]=>([(0,5),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5),(5,6)],7) [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[4,3,2,5,6,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7) [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[3,4,5,2,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7) [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[2,5,4,3,6,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[3,5,4,6,2,7,1]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7) [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[2,4,5,6,3,7,1]=>([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7) [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[2,3,6,5,4,7,1]=>([(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[3,6,4,5,7,2,1]=>([(2,3),(2,4),(3,5),(4,6),(5,6)],7) [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[2,4,6,5,7,3,1]=>([(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7) [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[2,3,5,6,7,4,1]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7) [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[2,3,4,7,6,5,1]=>([(1,5),(5,6),(6,2),(6,3),(6,4)],7) [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[3,4,5,1,6,7,2]=>([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7) [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[2,5,4,1,6,7,3]=>([(0,5),(0,6),(1,2),(1,3),(1,5),(2,6),(3,6),(6,4)],7) [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[3,5,4,6,1,7,2]=>([(0,4),(0,6),(1,2),(1,3),(2,5),(3,5),(5,6)],7) [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[2,4,5,6,1,7,3]=>([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7) [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[2,3,6,5,1,7,4]=>([(0,5),(0,6),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5)],7) [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[3,6,4,5,7,1,2]=>([(0,4),(1,3),(1,5),(2,6),(3,6),(5,2)],7) [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[2,4,6,5,7,1,3]=>([(0,6),(1,4),(1,6),(2,5),(3,5),(4,2),(4,3)],7) [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[2,3,5,6,7,1,4]=>([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7) [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[2,3,4,7,6,1,5]=>([(0,6),(1,4),(4,5),(5,2),(5,3),(5,6)],7) [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[4,1,2,5,3,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[3,1,5,2,4,6,7]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[2,5,1,3,4,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[4,1,2,5,6,3,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[3,1,5,2,6,4,7]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[2,5,1,3,6,4,7]=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[3,1,4,6,2,5,7]=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[2,4,1,6,3,5,7]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[2,3,6,1,4,5,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[4,1,2,5,6,7,3]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[3,1,5,2,6,7,4]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[2,5,1,3,6,7,4]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[3,1,4,6,2,7,5]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[2,4,1,6,3,7,5]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[2,3,6,1,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[3,1,4,5,7,2,6]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[2,4,1,5,7,3,6]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[2,3,5,1,7,4,6]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[2,3,4,7,1,5,6]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[4,3,2,6,5,7,1]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[3,4,6,2,5,7,1]=>([(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[2,6,4,3,5,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[3,4,6,5,2,7,1]=>([(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[2,6,4,5,3,7,1]=>([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[4,3,2,5,7,6,1]=>([(1,6),(2,6),(3,6),(6,4),(6,5)],7) [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[3,4,5,2,7,6,1]=>([(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[2,5,4,3,7,6,1]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[3,5,4,7,2,6,1]=>([(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[2,4,5,7,3,6,1]=>([(1,3),(1,4),(3,6),(4,5),(5,2),(5,6)],7) [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[2,3,7,5,4,6,1]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[3,4,5,6,7,2,1]=>([(2,6),(4,5),(5,3),(6,4)],7) [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[2,5,4,6,7,3,1]=>([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[3,5,4,7,6,2,1]=>([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[2,4,5,7,6,3,1]=>([(1,4),(1,5),(5,6),(6,2),(6,3)],7) [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[2,3,7,5,6,4,1]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7) [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[3,4,5,6,7,1,2]=>([(0,6),(1,3),(4,5),(5,2),(6,4)],7) [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[2,5,4,6,7,1,3]=>([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7) [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[3,5,4,7,6,1,2]=>([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6)],7) [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[2,4,5,7,6,1,3]=>([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7) [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[2,3,7,5,6,1,4]=>([(0,6),(1,5),(4,3),(5,2),(5,4),(5,6)],7) [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[4,5,3,6,1,2,7]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[3,5,6,4,1,2,7]=>([(0,4),(1,3),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[2,6,5,4,1,3,7]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[3,4,6,1,5,2,7]=>([(0,4),(1,3),(1,5),(2,6),(3,6),(4,2),(4,5),(5,6)],7) [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[2,6,4,1,5,3,7]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7) [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[4,5,3,6,1,7,2]=>([(0,6),(1,4),(2,3),(2,5),(4,6),(6,5)],7) [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[3,5,6,4,1,7,2]=>([(0,4),(0,6),(1,3),(1,5),(2,6),(3,6),(5,2)],7) [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[2,6,5,4,1,7,3]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7) [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[3,4,6,1,5,7,2]=>([(0,3),(0,6),(1,4),(2,5),(4,2),(4,6),(6,5)],7) [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[2,6,4,1,5,7,3]=>([(0,2),(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(6,4)],7) [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[4,6,3,5,7,1,2]=>([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[3,6,5,4,7,1,2]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6)],7) [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[2,5,6,4,7,1,3]=>([(0,6),(1,3),(1,4),(1,6),(2,5),(3,5),(4,2)],7) [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[3,6,4,7,5,1,2]=>([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[2,4,6,7,5,1,3]=>([(0,6),(1,5),(1,6),(4,3),(5,2),(5,4)],7) [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[2,3,7,6,5,1,4]=>([(0,6),(1,5),(5,2),(5,3),(5,4),(5,6)],7) [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[3,4,5,1,7,6,2]=>([(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(4,2)],7) [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[2,5,4,1,7,6,3]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6)],7) [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[3,5,4,7,1,6,2]=>([(0,4),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6)],7) [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[2,4,5,7,1,6,3]=>([(0,5),(0,6),(1,3),(1,6),(3,4),(4,2),(4,5)],7) [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[2,3,7,5,1,6,4]=>([(0,5),(0,6),(1,4),(3,5),(4,2),(4,3),(4,6)],7) [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[5,4,2,3,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[4,5,2,6,3,1,7]=>([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[3,5,6,2,4,1,7]=>([(0,6),(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7) [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[2,6,5,3,4,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[4,5,2,6,1,3,7]=>([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[3,5,6,2,1,4,7]=>([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7) [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[2,6,5,3,1,4,7]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(5,6)],7) [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[3,4,6,1,2,5,7]=>([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[2,6,4,1,3,5,7]=>([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(5,4),(6,5)],7) [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[5,4,2,3,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7) [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[4,5,2,6,3,7,1]=>([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[3,5,6,2,4,7,1]=>([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7) [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[2,6,5,3,4,7,1]=>([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[4,6,2,5,7,3,1]=>([(1,3),(1,5),(2,4),(2,5),(4,6),(5,6)],7) [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[3,6,5,2,7,4,1]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[2,5,6,3,7,4,1]=>([(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[3,6,4,7,2,5,1]=>([(1,5),(2,3),(2,4),(3,6),(4,5),(4,6)],7) [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[2,4,6,7,3,5,1]=>([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[2,3,7,6,4,5,1]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7) [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[4,5,2,6,1,7,3]=>([(0,4),(0,6),(1,4),(1,5),(2,3),(3,6),(6,5)],7) [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[3,5,6,2,1,7,4]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[2,6,5,3,1,7,4]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(4,6)],7) [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[3,4,6,1,2,7,5]=>([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[2,6,4,1,3,7,5]=>([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[4,6,2,5,7,1,3]=>([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(5,6)],7) [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[3,6,5,2,7,1,4]=>([(0,5),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[2,5,6,3,7,1,4]=>([(0,6),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2)],7) [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[3,6,4,7,2,1,5]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7) [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[2,4,6,7,3,1,5]=>([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[2,3,7,6,4,1,5]=>([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7) [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[3,4,5,1,7,2,6]=>([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7) [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[2,5,4,1,7,3,6]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[3,5,4,7,1,2,6]=>([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,6)],7) [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[2,4,5,7,1,3,6]=>([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[2,3,7,5,1,4,6]=>([(0,6),(1,4),(3,5),(4,2),(4,3),(4,6),(6,5)],7) [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[5,1,2,3,6,4,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[4,1,2,6,3,5,7]=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[3,1,6,2,4,5,7]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[2,6,1,3,4,5,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[5,1,2,3,6,7,4]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[4,1,2,6,3,7,5]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[3,1,6,2,4,7,5]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[2,6,1,3,4,7,5]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[4,1,2,5,7,3,6]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[3,1,5,2,7,4,6]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[2,5,1,3,7,4,6]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[3,1,4,7,2,5,6]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[2,4,1,7,3,5,6]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[2,3,7,1,4,5,6]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[5,6,4,3,7,1,2]=>([(0,6),(1,6),(2,4),(3,5),(5,6)],7) [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[4,6,5,7,3,1,2]=>([(1,3),(2,4),(2,5),(4,6),(5,6)],7) [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[3,6,7,5,4,1,2]=>([(0,5),(1,3),(1,4),(1,6),(6,2)],7) [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[2,7,6,5,4,1,3]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[4,5,6,7,1,3,2]=>([(0,6),(1,3),(1,4),(5,2),(6,5)],7) [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[3,5,7,6,1,4,2]=>([(0,4),(0,6),(1,5),(1,6),(5,2),(5,3)],7) [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[2,7,5,6,1,4,3]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(4,2)],7) [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[3,4,7,1,6,5,2]=>([(0,4),(1,3),(1,5),(1,6),(4,2),(4,5),(4,6)],7) [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[2,7,4,1,6,5,3]=>([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5)],7) [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[4,5,6,7,1,2,3]=>([(0,5),(1,6),(4,3),(5,4),(6,2)],7) [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[3,5,7,6,1,2,4]=>([(0,4),(1,5),(1,6),(4,6),(5,2),(5,3)],7) [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[2,7,5,6,1,3,4]=>([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7) [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[3,4,7,1,6,2,5]=>([(0,3),(0,6),(1,4),(3,5),(4,2),(4,5),(4,6)],7) [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[2,7,4,1,6,3,5]=>([(0,2),(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(6,4)],7) [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[6,5,2,3,4,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[5,6,2,3,7,4,1]=>([(1,3),(2,4),(3,6),(4,5),(4,6)],7) [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[4,6,2,7,3,5,1]=>([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[3,6,7,2,4,5,1]=>([(1,6),(2,3),(2,6),(3,5),(6,4)],7) [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[2,7,6,3,4,5,1]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7) [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[5,6,2,3,7,1,4]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(4,6)],7) [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[4,6,2,7,3,1,5]=>([(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[3,6,7,2,4,1,5]=>([(0,6),(1,5),(2,3),(2,5),(3,4),(5,6)],7) [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[2,7,6,3,4,1,5]=>([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7) [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[4,5,2,7,1,3,6]=>([(0,4),(1,4),(1,5),(2,3),(3,5),(3,6),(4,6)],7) [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[3,5,7,2,1,4,6]=>([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7) [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[2,7,5,3,1,4,6]=>([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[3,4,7,1,2,5,6]=>([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7) [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[2,7,4,1,3,5,6]=>([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,7,4,6]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[4,1,2,7,3,5,6]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[3,1,7,2,4,5,6]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[2,7,1,3,4,5,6]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],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]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$