Identifier
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Images
=>
Cc0007;cc-rep-0Cc0002;cc-rep-3
[[1]]=>[1]=>[1]=>[1] [[1,2]]=>[1,2]=>[1,2]=>[1,1] [[1],[2]]=>[2,1]=>[2,1]=>[2] [[1,2,3]]=>[1,2,3]=>[1,2,3]=>[1,1,1] [[1,3],[2]]=>[2,1,3]=>[2,3,1]=>[3] [[1,2],[3]]=>[3,1,2]=>[1,3,2]=>[2,1] [[1],[2],[3]]=>[3,2,1]=>[3,2,1]=>[2,1] [[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[1,1,1,1] [[1,3,4],[2]]=>[2,1,3,4]=>[2,3,4,1]=>[4] [[1,2,4],[3]]=>[3,1,2,4]=>[1,3,4,2]=>[3,1] [[1,2,3],[4]]=>[4,1,2,3]=>[1,2,4,3]=>[2,1,1] [[1,3],[2,4]]=>[2,4,1,3]=>[2,4,1,3]=>[4] [[1,2],[3,4]]=>[3,4,1,2]=>[3,4,1,2]=>[2,2] [[1,4],[2],[3]]=>[3,2,1,4]=>[3,4,2,1]=>[4] [[1,3],[2],[4]]=>[4,2,1,3]=>[2,4,3,1]=>[3,1] [[1,2],[3],[4]]=>[4,3,1,2]=>[1,4,3,2]=>[2,1,1] [[1],[2],[3],[4]]=>[4,3,2,1]=>[4,3,2,1]=>[2,2] [[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,1,1,1,1] [[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,3,4,5,1]=>[5] [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[1,3,4,5,2]=>[4,1] [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[1,2,4,5,3]=>[3,1,1] [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[1,2,3,5,4]=>[2,1,1,1] [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[2,4,5,1,3]=>[3,2] [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[3,4,5,1,2]=>[5] [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[2,3,5,1,4]=>[5] [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[1,3,5,2,4]=>[4,1] [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[1,4,5,2,3]=>[2,2,1] [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[3,2] [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[5] [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[1,4,5,3,2]=>[4,1] [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[2,3,5,4,1]=>[4,1] [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[3,1,1] [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[2,1,1,1] [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[3,5,2,4,1]=>[4,1] [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[4,5,2,3,1]=>[5] [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[4,5,1,3,2]=>[3,2] [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[2,5,1,4,3]=>[4,1] [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[3,5,1,4,2]=>[2,2,1] [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[4,5,3,2,1]=>[4,1] [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[3,5,4,2,1]=>[5] [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[2,5,4,3,1]=>[3,2] [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[1,5,4,3,2]=>[2,2,1] [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[2,2,1] [[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1] [[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,3,4,5,6,1]=>[6] [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[1,3,4,5,6,2]=>[5,1] [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[1,2,4,5,6,3]=>[4,1,1] [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[1,2,3,5,6,4]=>[3,1,1,1] [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>[2,1,1,1,1] [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[2,4,5,6,1,3]=>[6] [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[3,4,5,6,1,2]=>[3,3] [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[2,3,5,6,1,4]=>[4,2] [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[1,3,5,6,2,4]=>[3,2,1] [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[1,4,5,6,2,3]=>[5,1] [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[2,3,4,6,1,5]=>[6] [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[1,3,4,6,2,5]=>[5,1] [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[1,2,4,6,3,5]=>[4,1,1] [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[1,2,5,6,3,4]=>[2,2,1,1] [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[3,4,5,6,2,1]=>[6] [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,5,6,3,1]=>[4,2] [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[1,4,5,6,3,2]=>[3,2,1] [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[2,3,5,6,4,1]=>[6] [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[1,3,5,6,4,2]=>[5,1] [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[1,2,5,6,4,3]=>[4,1,1] [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[2,3,4,6,5,1]=>[5,1] [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[1,3,4,6,5,2]=>[4,1,1] [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[1,2,4,6,5,3]=>[3,1,1,1] [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>[2,1,1,1,1] [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[2,4,6,1,3,5]=>[3,3] [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[3,4,6,1,2,5]=>[6] [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[2,5,6,1,3,4]=>[6] [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[3,5,6,1,2,4]=>[4,2] [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[2,2,2] [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[3,5,6,2,4,1]=>[3,3] [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[4,5,6,2,3,1]=>[6] [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[4,5,6,1,3,2]=>[4,2] [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[2,5,6,1,4,3]=>[4,2] [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[3,5,6,1,4,2]=>[6] [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[3,4,6,2,5,1]=>[3,2,1] [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[2,4,6,3,5,1]=>[5,1] [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[1,4,6,3,5,2]=>[4,1,1] [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[2,5,6,3,4,1]=>[6] [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[1,5,6,3,4,2]=>[5,1] [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[1,5,6,2,4,3]=>[3,2,1] [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[2,4,6,1,5,3]=>[3,2,1] [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[3,4,6,1,5,2]=>[5,1] [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[2,3,6,1,5,4]=>[5,1] [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[1,3,6,2,5,4]=>[4,1,1] [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[1,4,6,2,5,3]=>[2,2,1,1] [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[4,5,6,3,2,1]=>[4,2] [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[3,5,6,4,2,1]=>[3,2,1] [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[2,5,6,4,3,1]=>[5,1] [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[1,5,6,4,3,2]=>[4,1,1] [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[3,4,6,5,2,1]=>[3,3] [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[2,4,6,5,3,1]=>[6] [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[1,4,6,5,3,2]=>[5,1] [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[2,3,6,5,4,1]=>[4,2] [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[1,3,6,5,4,2]=>[3,2,1] [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>[2,2,1,1] [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[3,6,2,5,1,4]=>[6] [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[4,6,2,5,1,3]=>[3,3] [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[4,6,3,5,1,2]=>[3,2,1] [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[5,6,2,4,1,3]=>[3,2,1] [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[2,2,1,1] [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[4,6,3,5,2,1]=>[5,1] [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[5,6,3,4,2,1]=>[4,1,1] [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[5,6,2,4,3,1]=>[5,1] [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[5,6,1,4,3,2]=>[3,2,1] [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[3,6,2,5,4,1]=>[4,2] [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[4,6,2,5,3,1]=>[6] [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[4,6,1,5,3,2]=>[4,2] [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[2,6,1,5,4,3]=>[4,2] [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[3,6,1,5,4,2]=>[2,2,2] [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[5,6,4,3,2,1]=>[4,2] [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[4,6,5,3,2,1]=>[6] [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[3,6,5,4,2,1]=>[5,1] [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[2,6,5,4,3,1]=>[3,2,1] [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>[2,2,1,1] [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[2,2,2] [[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1] [[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>[7] [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[1,3,4,5,6,7,2]=>[6,1] [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[1,2,4,5,6,7,3]=>[5,1,1] [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[1,2,3,5,6,7,4]=>[4,1,1,1] [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,7,5]=>[3,1,1,1,1] [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>[2,1,1,1,1,1] [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[2,4,5,6,7,1,3]=>[4,3] [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[3,4,5,6,7,1,2]=>[7] [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[2,3,5,6,7,1,4]=>[7] [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[1,3,5,6,7,2,4]=>[6,1] [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[1,4,5,6,7,2,3]=>[3,3,1] [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[2,3,4,6,7,1,5]=>[5,2] [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[1,3,4,6,7,2,5]=>[4,2,1] [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[1,2,4,6,7,3,5]=>[3,2,1,1] [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[1,2,5,6,7,3,4]=>[5,1,1] [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[2,3,4,5,7,1,6]=>[7] [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[1,3,4,5,7,2,6]=>[6,1] [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[1,2,4,5,7,3,6]=>[5,1,1] [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[1,2,3,5,7,4,6]=>[4,1,1,1] [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[1,2,3,6,7,4,5]=>[2,2,1,1,1] [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[3,4,5,6,7,2,1]=>[4,3] [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[2,4,5,6,7,3,1]=>[7] [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[1,4,5,6,7,3,2]=>[6,1] [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[2,3,5,6,7,4,1]=>[5,2] [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[1,3,5,6,7,4,2]=>[4,2,1] [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[1,2,5,6,7,4,3]=>[3,2,1,1] [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[2,3,4,6,7,5,1]=>[7] [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[1,3,4,6,7,5,2]=>[6,1] [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[1,2,4,6,7,5,3]=>[5,1,1] [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[1,2,3,6,7,5,4]=>[4,1,1,1] [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[2,3,4,5,7,6,1]=>[6,1] [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[1,3,4,5,7,6,2]=>[5,1,1] [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[1,2,4,5,7,6,3]=>[4,1,1,1] [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[1,2,3,5,7,6,4]=>[3,1,1,1,1] [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>[2,1,1,1,1,1] [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[2,4,6,7,1,3,5]=>[5,2] [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[3,4,6,7,1,2,5]=>[7] [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[2,5,6,7,1,3,4]=>[3,2,2] [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[3,5,6,7,1,2,4]=>[5,2] [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[4,5,6,7,1,2,3]=>[7] [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[2,4,5,7,1,3,6]=>[7] [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[3,4,5,7,1,2,6]=>[4,3] [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[2,3,5,7,1,4,6]=>[4,3] [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[1,3,5,7,2,4,6]=>[3,3,1] [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[1,4,5,7,2,3,6]=>[6,1] [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[2,3,6,7,1,4,5]=>[7] [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[1,3,6,7,2,4,5]=>[6,1] [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[1,4,6,7,2,3,5]=>[4,2,1] [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[1,5,6,7,2,3,4]=>[2,2,2,1] [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[3,5,6,7,2,4,1]=>[5,2] [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[4,5,6,7,2,3,1]=>[3,2,2] [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[4,5,6,7,1,3,2]=>[5,2] [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[2,5,6,7,1,4,3]=>[4,3] [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[3,5,6,7,1,4,2]=>[7] [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[3,4,6,7,2,5,1]=>[7] [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[2,4,6,7,3,5,1]=>[4,3] [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[1,4,6,7,3,5,2]=>[3,3,1] [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[2,5,6,7,3,4,1]=>[7] [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[1,5,6,7,3,4,2]=>[6,1] [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[1,5,6,7,2,4,3]=>[4,2,1] [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[2,4,6,7,1,5,3]=>[7] [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[3,4,6,7,1,5,2]=>[4,3] [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[2,3,6,7,1,5,4]=>[5,2] [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[1,3,6,7,2,5,4]=>[4,2,1] [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[1,4,6,7,2,5,3]=>[6,1] [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[3,4,5,7,2,6,1]=>[6,1] [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[2,4,5,7,3,6,1]=>[4,2,1] [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[1,4,5,7,3,6,2]=>[3,2,1,1] [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[2,3,5,7,4,6,1]=>[6,1] [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[1,3,5,7,4,6,2]=>[5,1,1] [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[1,2,5,7,4,6,3]=>[4,1,1,1] [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[2,3,6,7,4,5,1]=>[7] [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[1,3,6,7,4,5,2]=>[6,1] [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[1,2,6,7,4,5,3]=>[5,1,1] [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[1,2,6,7,3,5,4]=>[3,2,1,1] [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[2,4,5,7,1,6,3]=>[6,1] [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[3,4,5,7,1,6,2]=>[3,3,1] [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[2,3,5,7,1,6,4]=>[4,2,1] [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[1,3,5,7,2,6,4]=>[3,2,1,1] [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[1,4,5,7,2,6,3]=>[5,1,1] [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[2,3,4,7,1,6,5]=>[6,1] [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[1,3,4,7,2,6,5]=>[5,1,1] [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[1,2,4,7,3,6,5]=>[4,1,1,1] [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[1,2,5,7,3,6,4]=>[2,2,1,1,1] [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[4,3] [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[7] [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[2,5,6,7,4,3,1]=>[5,2] [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[1,5,6,7,4,3,2]=>[4,2,1] [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[3,4,6,7,5,2,1]=>[6,1] [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[4,2,1] [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[1,4,6,7,5,3,2]=>[3,2,1,1] [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[6,1] [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[1,3,6,7,5,4,2]=>[5,1,1] [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[1,2,6,7,5,4,3]=>[4,1,1,1] [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[3,4,5,7,6,2,1]=>[7] [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[2,4,5,7,6,3,1]=>[4,3] [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[3,3,1] [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[2,3,5,7,6,4,1]=>[7] [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[6,1] [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[1,2,5,7,6,4,3]=>[5,1,1] [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[2,3,4,7,6,5,1]=>[5,2] [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[1,3,4,7,6,5,2]=>[4,2,1] [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[3,2,1,1] [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[2,2,1,1,1] [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[3,5,7,2,4,6,1]=>[3,3,1] [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[4,5,7,2,3,6,1]=>[6,1] [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[4,5,7,1,3,6,2]=>[4,2,1] [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[2,5,7,1,4,6,3]=>[4,2,1] [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[3,5,7,1,4,6,2]=>[6,1] [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[3,6,7,2,4,5,1]=>[4,3] [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[4,6,7,2,3,5,1]=>[7] [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[4,6,7,1,3,5,2]=>[5,2] [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[5,6,7,2,3,4,1]=>[4,3] [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[5,6,7,1,3,4,2]=>[7] [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[5,6,7,1,2,4,3]=>[5,2] [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[2,6,7,1,4,5,3]=>[5,2] [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[3,6,7,1,4,5,2]=>[7] [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[2,6,7,1,3,5,4]=>[7] [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[3,6,7,1,2,5,4]=>[4,3] [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[4,6,7,1,2,5,3]=>[3,2,2] [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[2,4,7,1,3,6,5]=>[3,3,1] [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[3,4,7,1,2,6,5]=>[6,1] [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[2,5,7,1,3,6,4]=>[6,1] [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[3,5,7,1,2,6,4]=>[4,2,1] [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[4,5,7,1,2,6,3]=>[2,2,2,1] [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[3,6,7,2,5,1,4]=>[6,1] [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[4,6,7,2,5,1,3]=>[4,2,1] [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[4,6,7,3,5,1,2]=>[6,1] [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[5,6,7,2,4,1,3]=>[5,2] [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[5,6,7,3,4,1,2]=>[7] [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[3,5,7,2,6,1,4]=>[7] [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[4,5,7,2,6,1,3]=>[5,2] [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[4,5,7,3,6,1,2]=>[7] [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[2,5,7,4,6,1,3]=>[4,2,1] [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[3,5,7,4,6,1,2]=>[6,1] [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[3,4,7,2,6,1,5]=>[5,2] [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[2,4,7,3,6,1,5]=>[7] [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[1,4,7,3,6,2,5]=>[6,1] [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[2,5,7,3,6,1,4]=>[4,3] [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[1,5,7,3,6,2,4]=>[3,3,1] [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[1,5,7,4,6,2,3]=>[3,2,1,1] [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[2,6,7,4,5,1,3]=>[3,2,1,1] [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[3,6,7,4,5,1,2]=>[5,1,1] [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[2,6,7,3,5,1,4]=>[3,3,1] [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[1,6,7,3,5,2,4]=>[3,2,1,1] [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[1,6,7,4,5,2,3]=>[2,2,1,1,1] [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[4,6,7,3,5,2,1]=>[4,2,1] [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[5,6,7,3,4,2,1]=>[5,2] [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[5,6,7,2,4,3,1]=>[7] [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[5,6,7,1,4,3,2]=>[4,3] [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[3,6,7,2,5,4,1]=>[3,3,1] [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[4,6,7,2,5,3,1]=>[6,1] [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[4,6,7,1,5,3,2]=>[4,2,1] [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[2,6,7,1,5,4,3]=>[4,2,1] [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[3,6,7,1,5,4,2]=>[6,1] [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[4,5,7,3,6,2,1]=>[4,3] [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[3,5,7,4,6,2,1]=>[3,3,1] [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[2,5,7,4,6,3,1]=>[6,1] [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[1,5,7,4,6,3,2]=>[5,1,1] [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[3,6,7,4,5,2,1]=>[3,2,1,1] [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[2,6,7,4,5,3,1]=>[5,1,1] [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[1,6,7,4,5,3,2]=>[4,1,1,1] [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[2,6,7,3,5,4,1]=>[6,1] [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[1,6,7,3,5,4,2]=>[5,1,1] [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[1,6,7,2,5,4,3]=>[3,2,1,1] [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[3,5,7,2,6,4,1]=>[4,3] [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[4,5,7,2,6,3,1]=>[7] [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[4,5,7,1,6,3,2]=>[5,2] [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[2,5,7,1,6,4,3]=>[5,2] [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[3,5,7,1,6,4,2]=>[7] [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[3,4,7,2,6,5,1]=>[3,2,2] [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[2,4,7,3,6,5,1]=>[5,2] [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[1,4,7,3,6,5,2]=>[4,2,1] [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[2,5,7,3,6,4,1]=>[7] [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[1,5,7,3,6,4,2]=>[6,1] [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[1,5,7,2,6,4,3]=>[4,2,1] [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[2,4,7,1,6,5,3]=>[3,2,2] [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[3,4,7,1,6,5,2]=>[5,2] [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[2,3,7,1,6,5,4]=>[5,2] [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[1,3,7,2,6,5,4]=>[4,2,1] [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[1,4,7,2,6,5,3]=>[2,2,2,1] [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[5,6,7,4,3,2,1]=>[4,2,1] [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[4,6,7,5,3,2,1]=>[5,2] [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[3,6,7,5,4,2,1]=>[3,2,2] [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[2,6,7,5,4,3,1]=>[5,2] [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[1,6,7,5,4,3,2]=>[4,2,1] [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[4,5,7,6,3,2,1]=>[7] [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[3,5,7,6,4,2,1]=>[4,3] [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[2,5,7,6,4,3,1]=>[7] [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[1,5,7,6,4,3,2]=>[6,1] [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[3,4,7,6,5,2,1]=>[3,3,1] [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[2,4,7,6,5,3,1]=>[6,1] [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[1,4,7,6,5,3,2]=>[5,1,1] [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[2,3,7,6,5,4,1]=>[4,2,1] [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[1,3,7,6,5,4,2]=>[3,2,1,1] [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>[2,2,1,1,1] [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[4,7,3,6,2,5,1]=>[6,1] [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[5,7,3,6,2,4,1]=>[4,2,1] [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[5,7,4,6,2,3,1]=>[4,3] [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[5,7,4,6,1,3,2]=>[3,2,2] [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[6,7,3,5,2,4,1]=>[6,1] [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[6,7,4,5,2,3,1]=>[7] [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[6,7,4,5,1,3,2]=>[5,2] [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[6,7,2,5,1,4,3]=>[4,3] [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[6,7,3,5,1,4,2]=>[4,2,1] [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[3,7,2,6,1,5,4]=>[7] [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[4,7,2,6,1,5,3]=>[4,3] [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[4,7,3,6,1,5,2]=>[4,2,1] [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[5,7,2,6,1,4,3]=>[3,2,2] [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[5,7,3,6,1,4,2]=>[2,2,2,1] [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[5,7,4,6,3,2,1]=>[7] [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[6,7,4,5,3,2,1]=>[4,3] [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[6,7,3,5,4,2,1]=>[4,2,1] [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[6,7,2,5,4,3,1]=>[5,2] [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[6,7,1,5,4,3,2]=>[3,2,2] [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[4,7,3,6,5,2,1]=>[5,1,1] [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[5,7,3,6,4,2,1]=>[6,1] [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[5,7,2,6,4,3,1]=>[7] [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[5,7,1,6,4,3,2]=>[5,2] [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[3,7,2,6,5,4,1]=>[4,2,1] [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[4,7,2,6,5,3,1]=>[6,1] [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[4,7,1,6,5,3,2]=>[4,2,1] [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[2,7,1,6,5,4,3]=>[4,2,1] [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[3,7,1,6,5,4,2]=>[2,2,2,1] [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[6,7,5,4,3,2,1]=>[4,2,1] [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[5,7,6,4,3,2,1]=>[6,1] [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[4,7,6,5,3,2,1]=>[7] [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[3,7,6,5,4,2,1]=>[5,2] [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[2,7,6,5,4,3,1]=>[3,2,2] [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>[2,2,2,1] [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,2,2,1] [[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1] [[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>[8] [[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,6,7,8,4]=>[5,1,1,1] [[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,8,6]=>[3,1,1,1,1,1] [[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>[2,1,1,1,1,1,1] [[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[3,4,5,6,7,8,1,2]=>[4,4] [[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[1,3,5,6,7,8,2,4]=>[4,3,1] [[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[1,3,4,5,7,8,2,6]=>[5,2,1] [[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[1,2,3,5,7,8,4,6]=>[3,2,1,1,1] [[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[1,2,3,6,7,8,4,5]=>[5,1,1,1] [[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[1,2,4,5,6,8,3,7]=>[6,1,1] [[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[1,2,3,5,6,8,4,7]=>[5,1,1,1] [[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,7,8,5,6]=>[2,2,1,1,1,1] [[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[2,3,5,6,7,8,4,1]=>[8] [[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[1,3,5,6,7,8,4,2]=>[7,1] [[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[1,2,5,6,7,8,4,3]=>[6,1,1] [[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,7,8,5,4]=>[3,2,1,1,1] [[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[1,2,3,5,7,8,6,4]=>[5,1,1,1] [[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[1,2,3,5,6,8,7,4]=>[4,1,1,1,1] [[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[1,3,5,7,8,2,4,6]=>[5,2,1] [[1,3,4,5,8],[2,6,7]]=>[2,6,7,1,3,4,5,8]=>[2,3,6,7,8,1,4,5]=>[4,2,2] [[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[1,5,6,7,8,2,3,4]=>[7,1] [[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[1,3,4,6,8,2,5,7]=>[4,3,1] [[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[1,2,4,6,8,3,5,7]=>[3,3,1,1] [[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[1,2,5,6,8,3,4,7]=>[6,1,1] [[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[1,2,5,7,8,3,4,6]=>[4,2,1,1] [[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[1,2,6,7,8,3,4,5]=>[2,2,2,1,1] [[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[1,2,5,7,8,4,6,3]=>[3,3,1,1] [[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[1,2,6,7,8,3,5,4]=>[4,2,1,1] [[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[1,2,5,7,8,3,6,4]=>[6,1,1] [[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[1,2,5,6,8,4,7,3]=>[3,2,1,1,1] [[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[2,3,4,6,8,5,7,1]=>[7,1] [[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[1,2,3,6,8,5,7,4]=>[4,1,1,1,1] [[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[1,2,3,7,8,5,6,4]=>[5,1,1,1] [[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[1,2,3,7,8,4,6,5]=>[3,2,1,1,1] [[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[3,4,5,6,8,1,7,2]=>[7,1] [[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[1,2,5,6,8,3,7,4]=>[5,1,1,1] [[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[1,2,3,5,8,4,7,6]=>[4,1,1,1,1] [[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[1,2,3,6,8,4,7,5]=>[2,2,1,1,1,1] [[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[4,5,6,7,8,3,2,1]=>[6,2] [[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[3,5,6,7,8,4,2,1]=>[8] [[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[2,5,6,7,8,4,3,1]=>[4,4] [[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[1,5,6,7,8,4,3,2]=>[4,3,1] [[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[1,4,6,7,8,5,3,2]=>[7,1] [[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[1,3,5,7,8,6,4,2]=>[4,2,1,1] [[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,8,6,5,4]=>[4,1,1,1,1] [[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[1,2,4,6,8,7,5,3]=>[6,1,1] [[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1] [[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[2,3,4,5,8,7,6,1]=>[6,2] [[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[1,2,3,5,8,7,6,4]=>[3,2,1,1,1] [[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>[2,2,1,1,1,1] [[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[2,4,6,8,1,3,5,7]=>[6,2] [[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[4,5,6,8,1,2,3,7]=>[8] [[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[3,5,7,8,1,2,4,6]=>[8] [[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[2,6,7,8,1,3,4,5]=>[8] [[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[3,6,7,8,1,2,4,5]=>[6,2] [[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[4,6,7,8,1,2,3,5]=>[4,2,2] [[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>[2,2,2,2] [[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[5,6,7,8,2,3,4,1]=>[8] [[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>[3,5,6,8,2,4,7,1]=>[5,2,1] [[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[2,5,6,8,1,4,7,3]=>[4,3,1] [[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>[3,4,6,8,2,5,7,1]=>[7,1] [[1,3,5,7],[2,6,8],[4]]=>[4,2,6,8,1,3,5,7]=>[2,4,6,8,3,5,7,1]=>[4,3,1] [[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[2,4,6,8,1,5,7,3]=>[7,1] [[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>[2,3,6,8,1,5,7,4]=>[5,2,1] [[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[3,4,7,8,2,5,6,1]=>[8] [[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[1,5,7,8,2,4,6,3]=>[5,2,1] [[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>[1,6,7,8,2,4,5,3]=>[7,1] [[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[1,6,7,8,2,3,5,4]=>[5,2,1] [[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[1,5,7,8,2,3,6,4]=>[3,2,2,1] [[1,3,5,6],[2,4,7],[8]]=>[8,2,4,7,1,3,5,6]=>[2,4,5,8,1,3,7,6]=>[7,1] [[1,3,4,6],[2,5,7],[8]]=>[8,2,5,7,1,3,4,6]=>[2,3,5,8,1,4,7,6]=>[4,3,1] [[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[2,3,6,8,1,4,7,5]=>[7,1] [[1,2,3,5],[4,6,7],[8]]=>[8,4,6,7,1,2,3,5]=>[1,4,6,8,2,3,7,5]=>[4,2,1,1] [[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[1,5,6,8,2,3,7,4]=>[2,2,2,1,1] [[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[3,4,7,8,2,6,1,5]=>[4,3,1] [[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[1,5,6,8,3,7,2,4]=>[5,2,1] [[1,2,5,7],[3,4],[6,8]]=>[6,8,3,4,1,2,5,7]=>[3,4,6,8,5,7,1,2]=>[4,3,1] [[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[3,4,5,8,2,7,1,6]=>[8] [[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[2,4,5,8,3,7,1,6]=>[6,2] [[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[1,3,5,8,4,7,2,6]=>[7,1] [[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[1,2,5,8,4,7,3,6]=>[6,1,1] [[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[2,3,6,8,4,7,1,5]=>[5,3] [[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[2,4,7,8,5,6,1,3]=>[6,1,1] [[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[2,3,7,8,5,6,1,4]=>[4,2,1,1] [[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[1,3,7,8,5,6,2,4]=>[3,2,1,1,1] [[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[1,2,7,8,5,6,3,4]=>[2,2,1,1,1,1] [[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[4,6,7,8,3,5,2,1]=>[5,3] [[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[5,6,7,8,3,4,2,1]=>[8] [[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[2,6,7,8,1,5,4,3]=>[4,4] [[1,5,6,8],[2,7],[3],[4]]=>[4,3,2,7,1,5,6,8]=>[4,5,7,8,3,6,2,1]=>[4,3,1] [[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[3,5,7,8,4,6,2,1]=>[7,1] [[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[3,6,7,8,4,5,2,1]=>[8] [[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[1,6,7,8,4,5,3,2]=>[5,2,1] [[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[1,5,7,8,3,6,4,2]=>[6,1,1] [[1,2,4,8],[3,5],[6],[7]]=>[7,6,3,5,1,2,4,8]=>[1,3,7,8,2,6,5,4]=>[4,2,1,1] [[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[4,5,6,8,3,7,2,1]=>[5,3] [[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[3,5,6,8,4,7,2,1]=>[8] [[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[3,4,6,8,5,7,2,1]=>[7,1] [[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[2,4,7,8,5,6,3,1]=>[4,2,1,1] [[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[1,3,7,8,5,6,4,2]=>[5,1,1,1] [[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[1,2,7,8,3,6,5,4]=>[3,2,1,1,1] [[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[2,4,5,8,3,7,6,1]=>[4,2,2] [[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[1,2,5,8,4,7,6,3]=>[4,2,1,1] [[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[1,3,6,8,4,7,5,2]=>[7,1] [[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[2,4,5,8,1,7,6,3]=>[6,2] [[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[2,3,5,8,1,7,6,4]=>[4,2,2] [[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[1,3,5,8,2,7,6,4]=>[3,2,2,1] [[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[2,3,4,8,1,7,6,5]=>[6,2] [[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[1,3,4,8,2,7,6,5]=>[5,2,1] [[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[1,2,4,8,3,7,6,5]=>[4,2,1,1] [[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[1,2,5,8,3,7,6,4]=>[2,2,2,1,1] [[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[5,6,7,8,4,3,2,1]=>[4,4] [[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[1,6,7,8,5,4,3,2]=>[4,2,1,1] [[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[3,5,7,8,6,4,2,1]=>[8] [[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[4,5,6,8,7,3,2,1]=>[3,3,2] [[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[2,4,6,8,7,5,3,1]=>[4,4] [[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[2,3,5,8,7,6,4,1]=>[7,1] [[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[1,3,5,8,7,6,4,2]=>[6,1,1] [[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[2,3,4,8,7,6,5,1]=>[5,2,1] [[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[1,3,4,8,7,6,5,2]=>[4,2,1,1] [[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[1,2,4,8,7,6,5,3]=>[3,2,1,1,1] [[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>[2,2,1,1,1,1] [[1,2,7],[3,5,8],[4,6]]=>[4,6,3,5,8,1,2,7]=>[4,6,8,3,5,7,1,2]=>[7,1] [[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[5,6,8,2,4,7,1,3]=>[6,2] [[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[4,7,8,3,5,6,1,2]=>[6,1,1] [[1,4,5],[2,6,8],[3,7]]=>[3,7,2,6,8,1,4,5]=>[3,7,8,2,4,6,1,5]=>[7,1] [[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[6,7,8,1,3,5,2,4]=>[6,2] [[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[6,7,8,1,4,5,2,3]=>[4,2,2] [[1,3,6],[2,5,7],[4,8]]=>[4,8,2,5,7,1,3,6]=>[4,5,8,2,3,7,1,6]=>[8] [[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[3,6,8,2,4,7,1,5]=>[8] [[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[2,6,8,1,5,7,3,4]=>[7,1] [[1,2,4],[3,5,7],[6,8]]=>[6,8,3,5,7,1,2,4]=>[3,6,8,1,5,7,2,4]=>[4,3,1] [[1,2,3],[4,5,7],[6,8]]=>[6,8,4,5,7,1,2,3]=>[4,6,8,1,5,7,2,3]=>[3,2,2,1] [[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[2,7,8,1,4,6,3,5]=>[7,1] [[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[2,7,8,1,5,6,3,4]=>[6,1,1] [[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[3,7,8,1,5,6,2,4]=>[4,2,1,1] [[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[4,6,8,3,5,7,2,1]=>[4,3,1] [[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[4,7,8,3,5,6,2,1]=>[4,2,1,1] [[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[6,7,8,3,4,5,2,1]=>[6,2] [[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[6,7,8,1,4,5,3,2]=>[4,4] [[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>[6,7,8,2,3,5,4,1]=>[5,3] [[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[6,7,8,1,2,5,4,3]=>[6,2] [[1,2,4],[3,5,8],[6],[7]]=>[7,6,3,5,8,1,2,4]=>[3,7,8,1,2,6,5,4]=>[4,3,1] [[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[4,7,8,1,2,6,5,3]=>[3,2,2,1] [[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[4,5,8,2,3,7,6,1]=>[6,2] [[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[3,6,8,1,2,7,5,4]=>[4,4] [[1,2,3],[4,5,7],[6],[8]]=>[8,6,4,5,7,1,2,3]=>[4,6,8,1,2,7,5,3]=>[4,2,2] [[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[2,4,8,1,3,7,6,5]=>[3,3,2] [[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[3,4,8,1,2,7,6,5]=>[6,2] [[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[4,7,8,3,6,2,5,1]=>[4,4] [[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[4,6,8,3,7,2,5,1]=>[4,2,2] [[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[3,6,8,5,7,1,4,2]=>[5,3] [[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[4,5,8,3,7,2,6,1]=>[4,4] [[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[4,7,8,5,6,1,3,2]=>[4,4] [[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[2,7,8,5,6,1,4,3]=>[6,2] [[1,2,6],[3,4],[5,8],[7]]=>[7,5,8,3,4,1,2,6]=>[3,7,8,5,6,1,4,2]=>[8] [[1,4,5],[2,6],[3,8],[7]]=>[7,3,8,2,6,1,4,5]=>[3,7,8,4,6,2,5,1]=>[4,3,1] [[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[2,7,8,5,6,3,4,1]=>[8] [[1,2,4],[3,6],[5,8],[7]]=>[7,5,8,3,6,1,2,4]=>[1,7,8,5,6,3,4,2]=>[7,1] [[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[3,6,8,2,7,1,5,4]=>[6,2] [[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[5,6,8,3,7,1,4,2]=>[8] [[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[3,4,8,2,7,1,6,5]=>[6,2] [[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[2,4,8,3,7,1,6,5]=>[8] [[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[1,4,8,3,7,2,6,5]=>[7,1] [[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[2,6,8,3,7,1,5,4]=>[3,3,2] [[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[1,6,8,3,7,2,5,4]=>[3,2,2,1] [[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[5,7,8,4,6,3,2,1]=>[5,2,1] [[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[6,7,8,1,5,4,3,2]=>[4,3,1] [[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>[3,6,8,5,7,4,2,1]=>[5,3] [[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>[3,7,8,5,6,4,2,1]=>[3,3,2] [[1,2,4],[3,8],[5],[6],[7]]=>[7,6,5,3,8,1,2,4]=>[1,7,8,3,6,5,4,2]=>[5,2,1] [[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[2,6,8,1,7,5,4,3]=>[6,2] [[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[3,5,8,4,7,6,2,1]=>[3,3,1,1] [[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[3,5,8,2,7,6,4,1]=>[4,3,1] [[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[3,5,8,1,7,6,4,2]=>[7,1] [[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[3,4,8,2,7,6,5,1]=>[3,2,2,1] [[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[2,5,8,3,7,6,4,1]=>[7,1] [[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[1,5,8,3,7,6,4,2]=>[6,1,1] [[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[1,5,8,2,7,6,4,3]=>[4,2,1,1] [[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[2,4,8,1,7,6,5,3]=>[3,2,2,1] [[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[1,3,8,2,7,6,5,4]=>[4,2,1,1] [[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[3,5,8,7,6,4,2,1]=>[5,3] [[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[3,4,8,7,6,5,2,1]=>[3,3,2] [[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[2,4,8,7,6,5,3,1]=>[6,2] [[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[1,4,8,7,6,5,3,2]=>[5,2,1] [[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[2,3,8,7,6,5,4,1]=>[4,2,2] [[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[1,3,8,7,6,5,4,2]=>[3,2,2,1] [[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>[2,2,2,1,1] [[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[4,8,3,7,2,6,1,5]=>[3,3,1,1] [[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[5,8,3,7,2,6,1,4]=>[6,1,1] [[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[5,8,4,7,2,6,1,3]=>[7,1] [[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[5,8,4,7,3,6,1,2]=>[5,2,1] [[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[6,8,3,7,2,5,1,4]=>[7,1] [[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[6,8,4,7,2,5,1,3]=>[8] [[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[6,8,4,7,3,5,1,2]=>[6,2] [[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[6,8,5,7,2,4,1,3]=>[4,4] [[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[6,8,5,7,3,4,1,2]=>[4,2,2] [[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[7,8,3,6,2,5,1,4]=>[5,2,1] [[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[7,8,4,6,2,5,1,3]=>[6,2] [[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[7,8,4,6,3,5,1,2]=>[4,2,2] [[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[7,8,5,6,2,4,1,3]=>[4,2,2] [[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2] [[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[6,8,4,7,3,5,2,1]=>[8] [[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[6,8,5,7,3,4,2,1]=>[6,2] [[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[7,8,5,6,3,4,2,1]=>[4,2,2] [[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[7,8,2,6,1,5,4,3]=>[5,3] [[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[5,8,3,7,2,6,4,1]=>[4,2,1,1] [[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[6,8,3,7,2,5,4,1]=>[5,2,1] [[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[6,8,4,7,2,5,3,1]=>[5,3] [[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[6,8,4,7,1,5,3,2]=>[3,3,2] [[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[3,8,2,7,1,6,5,4]=>[7,1] [[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[4,8,3,7,1,6,5,2]=>[4,2,1,1] [[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[5,8,2,7,1,6,4,3]=>[3,2,2,1] [[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[5,8,3,7,1,6,4,2]=>[2,2,2,1,1] [[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[6,8,5,7,4,3,2,1]=>[8] [[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[7,8,5,6,4,3,2,1]=>[4,4] [[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[7,8,1,6,5,4,3,2]=>[3,2,2,1] [[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[4,8,3,7,6,5,2,1]=>[5,2,1] [[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[5,8,2,7,6,4,3,1]=>[8] [[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[3,8,2,7,6,5,4,1]=>[4,2,2] [[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[2,8,1,7,6,5,4,3]=>[4,2,2] [[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[3,8,1,7,6,5,4,2]=>[2,2,2,2] [[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[7,8,6,5,4,3,2,1]=>[4,2,2] [[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[6,8,7,5,4,3,2,1]=>[6,2] [[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[5,8,7,6,4,3,2,1]=>[8] [[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[4,8,7,6,5,3,2,1]=>[7,1] [[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[3,8,7,6,5,4,2,1]=>[5,2,1] [[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[2,8,7,6,5,4,3,1]=>[3,2,2,1] [[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>[2,2,2,1,1] [[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,2,2,2] [[1,3,5,7,9],[2,4,6,8,10]]=>[2,4,6,8,10,1,3,5,7,9]=>[2,4,6,8,10,1,3,5,7,9]=>[10] [[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[12] [[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,1,1] [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2,2]
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
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
Map
cycle type
Description
The cycle type of a permutation as a partition.