Identifier
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0007;cc-rep-0Cc0009;cc-rep-3
[[1]]=>[1]=>[1]=>{{1}} [[1,2]]=>[1,2]=>[1,2]=>{{1},{2}} [[1],[2]]=>[2,1]=>[2,1]=>{{1,2}} [[1,2,3]]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}} [[1,3],[2]]=>[2,1,3]=>[2,1,3]=>{{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]=>{{1},{2},{3},{4}} [[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}} [[1,2,4],[3]]=>[3,1,2,4]=>[2,3,1,4]=>{{1,2,3},{4}} [[1,2,3],[4]]=>[4,1,2,3]=>[2,3,4,1]=>{{1,2,3,4}} [[1,3],[2,4]]=>[2,4,1,3]=>[3,2,4,1]=>{{1,3,4},{2}} [[1,2],[3,4]]=>[3,4,1,2]=>[2,4,3,1]=>{{1,2,4},{3}} [[1,4],[2],[3]]=>[3,2,1,4]=>[3,1,2,4]=>{{1,2,3},{4}} [[1,3],[2],[4]]=>[4,2,1,3]=>[3,1,4,2]=>{{1,2,3,4}} [[1,2],[3],[4]]=>[4,3,1,2]=>[2,4,1,3]=>{{1,2,3,4}} [[1],[2],[3],[4]]=>[4,3,2,1]=>[4,1,2,3]=>{{1,2,3,4}} [[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}} [[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}} [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}} [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}} [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}} [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}} [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[3,2,4,5,1]=>{{1,3,4,5},{2}} [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[2,4,3,5,1]=>{{1,2,4,5},{3}} [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[2,3,5,4,1]=>{{1,2,3,5},{4}} [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[3,1,2,4,5]=>{{1,2,3},{4},{5}} [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[3,1,4,2,5]=>{{1,2,3,4},{5}} [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[2,4,1,3,5]=>{{1,2,3,4},{5}} [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[3,1,4,5,2]=>{{1,2,3,4,5}} [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[2,4,1,5,3]=>{{1,2,3,4,5}} [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[2,3,5,1,4]=>{{1,2,3,4,5}} [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,3,2,5,1]=>{{1,4,5},{2,3}} [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[3,4,5,2,1]=>{{1,3,5},{2,4}} [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[2,5,4,3,1]=>{{1,2,5},{3,4}} [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[3,4,5,1,2]=>{{1,2,3,4,5}} [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[2,5,4,1,3]=>{{1,2,3,4,5}} [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[4,1,2,3,5]=>{{1,2,3,4},{5}} [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[4,1,2,5,3]=>{{1,2,3,4,5}} [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[3,1,5,2,4]=>{{1,2,3,4,5}} [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[2,5,1,3,4]=>{{1,2,3,4,5}} [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>{{1,2,3,4,5}} [[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}} [[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}} [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}} [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}} [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}} [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}} [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}} [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}} [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}} [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}} [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}} [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}} [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}} [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}} [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}} [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}} [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[2,4,1,3,5,6]=>{{1,2,3,4},{5},{6}} [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}} [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[2,4,1,5,3,6]=>{{1,2,3,4,5},{6}} [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[2,3,5,1,4,6]=>{{1,2,3,4,5},{6}} [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}} [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}} [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}} [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}} [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}} [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}} [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}} [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}} [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}} [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}} [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}} [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}} [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[3,4,5,1,2,6]=>{{1,2,3,4,5},{6}} [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[2,5,4,1,3,6]=>{{1,2,3,4,5},{6}} [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}} [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}} [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}} [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}} [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}} [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}} [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[3,4,5,1,6,2]=>{{1,2,3,4,5,6}} [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[2,5,4,1,6,3]=>{{1,2,3,4,5,6}} [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[3,5,4,6,1,2]=>{{1,2,3,4,5,6}} [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[2,4,5,6,1,3]=>{{1,2,3,4,5,6}} [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>{{1,2,3,4,5,6}} [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}} [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}} [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[3,1,5,2,4,6]=>{{1,2,3,4,5},{6}} [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[2,5,1,3,4,6]=>{{1,2,3,4,5},{6}} [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}} [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}} [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>{{1,2,3,4,5,6}} [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}} [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}} [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}} [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[4,5,3,6,1,2]=>{{1,2,4,5,6},{3}} [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,5,6,4,1,2]=>{{1,2,3,5,6},{4}} [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[2,6,5,4,1,3]=>{{1,2,3,5,6},{4}} [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[3,4,6,1,5,2]=>{{1,2,3,4,6},{5}} [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>{{1,2,3,4,6},{5}} [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}} [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[4,5,2,6,3,1]=>{{1,4,6},{2,3,5}} [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[3,5,6,2,4,1]=>{{1,3,6},{2,4,5}} [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>{{1,2,6},{3,4,5}} [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[4,5,2,6,1,3]=>{{1,2,3,4,5,6}} [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[3,5,6,2,1,4]=>{{1,2,3,4,5,6}} [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>{{1,2,3,4,5,6}} [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[3,4,6,1,2,5]=>{{1,2,3,4,5,6}} [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>{{1,2,3,4,5,6}} [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}} [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}} [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>{{1,2,3,4,5,6}} [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>{{1,2,3,4,5,6}} [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}} [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}} [[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}} [[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}} [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}} [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}} [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}} [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}} [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{6},{7}} [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}} [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}} [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}} [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}} [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}} [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}} [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}} [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}} [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}} [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}} [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[2,4,1,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[2,4,1,5,3,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[2,3,5,1,4,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}} [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[2,4,1,5,6,3,7]=>{{1,2,3,4,5,6},{7}} [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[2,3,5,1,6,4,7]=>{{1,2,3,4,5,6},{7}} [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[2,3,4,6,1,5,7]=>{{1,2,3,4,5,6},{7}} [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}} [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}} [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}} [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}} [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}} [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}} [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>{{1,2,5,6},{3},{4},{7}} [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}} [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}} [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}} [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}} [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}} [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}} [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}} [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}} [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}} [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}} [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}} [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}} [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}} [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}} [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}} [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[3,4,5,1,2,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[2,5,4,1,3,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}} [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}} [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}} [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[3,5,4,6,2,1,7]=>{{1,3,4,6},{2,5},{7}} [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[2,4,5,6,3,1,7]=>{{1,2,4,6},{3,5},{7}} [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}} [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[3,4,5,1,6,2,7]=>{{1,2,3,4,5,6},{7}} [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[2,5,4,1,6,3,7]=>{{1,2,3,4,5,6},{7}} [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[3,5,4,6,1,2,7]=>{{1,2,3,4,5,6},{7}} [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[2,4,5,6,1,3,7]=>{{1,2,3,4,5,6},{7}} [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[2,3,6,5,1,4,7]=>{{1,2,3,4,5,6},{7}} [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}} [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}} [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}} [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[3,5,4,6,2,7,1]=>{{1,3,4,6,7},{2,5}} [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[2,4,5,6,3,7,1]=>{{1,2,4,6,7},{3,5}} [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}} [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[3,6,4,5,7,2,1]=>{{1,3,4,5,7},{2,6}} [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[2,4,6,5,7,3,1]=>{{1,2,4,5,7},{3,6}} [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[2,3,5,6,7,4,1]=>{{1,2,3,5,7},{4,6}} [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}} [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[3,4,5,1,6,7,2]=>{{1,2,3,4,5,6,7}} [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}} [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[3,5,4,6,1,7,2]=>{{1,2,3,4,5,6,7}} [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[2,4,5,6,1,7,3]=>{{1,2,3,4,5,6,7}} [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}} [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[3,6,4,5,7,1,2]=>{{1,2,3,4,5,6,7}} [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[2,4,6,5,7,1,3]=>{{1,2,3,4,5,6,7}} [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[2,3,5,6,7,1,4]=>{{1,2,3,4,5,6,7}} [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}} [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[3,1,5,2,4,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[2,5,1,3,4,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}} [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[3,1,5,2,6,4,7]=>{{1,2,3,4,5,6},{7}} [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[2,5,1,3,6,4,7]=>{{1,2,3,4,5,6},{7}} [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[3,1,4,6,2,5,7]=>{{1,2,3,4,5,6},{7}} [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[2,4,1,6,3,5,7]=>{{1,2,3,4,5,6},{7}} [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[2,3,6,1,4,5,7]=>{{1,2,3,4,5,6},{7}} [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}} [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}} [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}} [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}} [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}} [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}} [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}} [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}} [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}} [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}} [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}} [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[3,4,6,2,5,7,1]=>{{1,3,6,7},{2,4},{5}} [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}} [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[3,4,6,5,2,7,1]=>{{1,3,6,7},{2,4,5}} [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}} [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}} [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[3,4,5,2,7,6,1]=>{{1,3,5,7},{2,4},{6}} [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}} [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[3,5,4,7,2,6,1]=>{{1,3,4,7},{2,5},{6}} [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[2,4,5,7,3,6,1]=>{{1,2,4,7},{3,5},{6}} [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}} [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}} [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[2,5,4,6,7,3,1]=>{{1,2,5,7},{3,4,6}} [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[3,5,4,7,6,2,1]=>{{1,3,4,7},{2,5,6}} [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[2,4,5,7,6,3,1]=>{{1,2,4,7},{3,5,6}} [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}} [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7}} [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[2,5,4,6,7,1,3]=>{{1,2,3,4,5,6,7}} [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[3,5,4,7,6,1,2]=>{{1,2,3,4,5,6,7}} [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[2,4,5,7,6,1,3]=>{{1,2,3,4,5,6,7}} [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}} [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[4,5,3,6,1,2,7]=>{{1,2,4,5,6},{3},{7}} [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[3,5,6,4,1,2,7]=>{{1,2,3,5,6},{4},{7}} [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[2,6,5,4,1,3,7]=>{{1,2,3,5,6},{4},{7}} [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[3,4,6,1,5,2,7]=>{{1,2,3,4,6},{5},{7}} [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[2,6,4,1,5,3,7]=>{{1,2,3,4,6},{5},{7}} [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[4,5,3,6,1,7,2]=>{{1,2,4,5,6,7},{3}} [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[3,5,6,4,1,7,2]=>{{1,2,3,5,6,7},{4}} [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[2,6,5,4,1,7,3]=>{{1,2,3,5,6,7},{4}} [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[3,4,6,1,5,7,2]=>{{1,2,3,4,6,7},{5}} [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[2,6,4,1,5,7,3]=>{{1,2,3,4,6,7},{5}} [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[4,6,3,5,7,1,2]=>{{1,2,4,5,6,7},{3}} [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[3,6,5,4,7,1,2]=>{{1,2,3,5,6,7},{4}} [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[2,5,6,4,7,1,3]=>{{1,2,3,5,6,7},{4}} [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[3,6,4,7,5,1,2]=>{{1,2,3,4,6,7},{5}} [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[2,4,6,7,5,1,3]=>{{1,2,3,4,6,7},{5}} [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[2,3,7,6,5,1,4]=>{{1,2,3,4,6,7},{5}} [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[3,4,5,1,7,6,2]=>{{1,2,3,4,5,7},{6}} [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[2,5,4,1,7,6,3]=>{{1,2,3,4,5,7},{6}} [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[3,5,4,7,1,6,2]=>{{1,2,3,4,5,7},{6}} [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[2,4,5,7,1,6,3]=>{{1,2,3,4,5,7},{6}} [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[2,3,7,5,1,6,4]=>{{1,2,3,4,5,7},{6}} [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[5,4,2,3,6,1,7]=>{{1,5,6},{2,3,4},{7}} [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[4,5,2,6,3,1,7]=>{{1,4,6},{2,3,5},{7}} [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[3,5,6,2,4,1,7]=>{{1,3,6},{2,4,5},{7}} [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[2,6,5,3,4,1,7]=>{{1,2,6},{3,4,5},{7}} [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[4,5,2,6,1,3,7]=>{{1,2,3,4,5,6},{7}} [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[3,5,6,2,1,4,7]=>{{1,2,3,4,5,6},{7}} [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[2,6,5,3,1,4,7]=>{{1,2,3,4,5,6},{7}} [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[3,4,6,1,2,5,7]=>{{1,2,3,4,5,6},{7}} [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[2,6,4,1,3,5,7]=>{{1,2,3,4,5,6},{7}} [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}} [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[4,5,2,6,3,7,1]=>{{1,4,6,7},{2,3,5}} [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[3,5,6,2,4,7,1]=>{{1,3,6,7},{2,4,5}} [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[2,6,5,3,4,7,1]=>{{1,2,6,7},{3,4,5}} [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[4,6,2,5,7,3,1]=>{{1,4,5,7},{2,3,6}} [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[3,6,5,2,7,4,1]=>{{1,3,5,7},{2,4,6}} [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[2,5,6,3,7,4,1]=>{{1,2,5,7},{3,4,6}} [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[3,6,4,7,2,5,1]=>{{1,3,4,7},{2,5,6}} [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[2,4,6,7,3,5,1]=>{{1,2,4,7},{3,5,6}} [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[2,3,7,6,4,5,1]=>{{1,2,3,7},{4,5,6}} [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[4,5,2,6,1,7,3]=>{{1,2,3,4,5,6,7}} [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[3,5,6,2,1,7,4]=>{{1,2,3,4,5,6,7}} [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[2,6,5,3,1,7,4]=>{{1,2,3,4,5,6,7}} [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[3,4,6,1,2,7,5]=>{{1,2,3,4,5,6,7}} [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[2,6,4,1,3,7,5]=>{{1,2,3,4,5,6,7}} [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[4,6,2,5,7,1,3]=>{{1,2,3,4,5,6,7}} [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[3,6,5,2,7,1,4]=>{{1,2,3,4,5,6,7}} [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[2,5,6,3,7,1,4]=>{{1,2,3,4,5,6,7}} [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[3,6,4,7,2,1,5]=>{{1,2,3,4,5,6,7}} [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[2,4,6,7,3,1,5]=>{{1,2,3,4,5,6,7}} [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[2,3,7,6,4,1,5]=>{{1,2,3,4,5,6,7}} [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[3,4,5,1,7,2,6]=>{{1,2,3,4,5,6,7}} [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[3,5,4,7,1,2,6]=>{{1,2,3,4,5,6,7}} [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[2,4,5,7,1,3,6]=>{{1,2,3,4,5,6,7}} [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[2,3,7,5,1,4,6]=>{{1,2,3,4,5,6,7}} [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}} [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}} [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[4,1,2,6,3,5,7]=>{{1,2,3,4,5,6},{7}} [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[3,1,6,2,4,5,7]=>{{1,2,3,4,5,6},{7}} [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[2,6,1,3,4,5,7]=>{{1,2,3,4,5,6},{7}} [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}} [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}} [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}} [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}} [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}} [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}} [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}} [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}} [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}} [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[5,6,4,3,7,1,2]=>{{1,2,5,6,7},{3,4}} [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[4,6,5,7,3,1,2]=>{{1,2,4,6,7},{3,5}} [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[3,6,7,5,4,1,2]=>{{1,2,3,6,7},{4,5}} [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[2,7,6,5,4,1,3]=>{{1,2,3,6,7},{4,5}} [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[4,5,6,7,1,3,2]=>{{1,2,4,5,7},{3,6}} [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[3,5,7,6,1,4,2]=>{{1,2,3,5,7},{4,6}} [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[2,7,5,6,1,4,3]=>{{1,2,3,5,7},{4,6}} [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[3,4,7,1,6,5,2]=>{{1,2,3,4,7},{5,6}} [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[2,7,4,1,6,5,3]=>{{1,2,3,4,7},{5,6}} [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[4,5,6,7,1,2,3]=>{{1,2,3,4,5,6,7}} [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[3,5,7,6,1,2,4]=>{{1,2,3,4,5,6,7}} [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[2,7,5,6,1,3,4]=>{{1,2,3,4,5,6,7}} [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[3,4,7,1,6,2,5]=>{{1,2,3,4,5,6,7}} [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[2,7,4,1,6,3,5]=>{{1,2,3,4,5,6,7}} [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}} [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[5,6,2,3,7,4,1]=>{{1,5,7},{2,3,4,6}} [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[4,6,2,7,3,5,1]=>{{1,4,7},{2,3,5,6}} [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[3,6,7,2,4,5,1]=>{{1,3,7},{2,4,5,6}} [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[2,7,6,3,4,5,1]=>{{1,2,7},{3,4,5,6}} [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[5,6,2,3,7,1,4]=>{{1,2,3,4,5,6,7}} [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[4,6,2,7,3,1,5]=>{{1,2,3,4,5,6,7}} [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[3,6,7,2,4,1,5]=>{{1,2,3,4,5,6,7}} [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[2,7,6,3,4,1,5]=>{{1,2,3,4,5,6,7}} [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[4,5,2,7,1,3,6]=>{{1,2,3,4,5,6,7}} [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[3,5,7,2,1,4,6]=>{{1,2,3,4,5,6,7}} [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[2,7,5,3,1,4,6]=>{{1,2,3,4,5,6,7}} [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[3,4,7,1,2,5,6]=>{{1,2,3,4,5,6,7}} [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[2,7,4,1,3,5,6]=>{{1,2,3,4,5,6,7}} [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}} [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}} [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}} [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}} [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}} [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}} [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}} [[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{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
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].