Identifier
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0007;cc-rep-0Cc0010;cc-rep-3
[[1]]=>[1]=>[1]=>[.,.] [[1,2]]=>[1,2]=>[1,2]=>[.,[.,.]] [[1],[2]]=>[2,1]=>[2,1]=>[[.,.],.] [[1,2,3]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [[1,3],[2]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [[1,2],[3]]=>[3,1,2]=>[2,3,1]=>[[.,.],[.,.]] [[1],[2],[3]]=>[3,2,1]=>[3,1,2]=>[[.,[.,.]],.] [[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [[1,2,4],[3]]=>[3,1,2,4]=>[2,3,1,4]=>[[.,.],[.,[.,.]]] [[1,2,3],[4]]=>[4,1,2,3]=>[2,3,4,1]=>[[.,.],[.,[.,.]]] [[1,3],[2,4]]=>[2,4,1,3]=>[3,2,4,1]=>[[[.,.],.],[.,.]] [[1,2],[3,4]]=>[3,4,1,2]=>[2,4,3,1]=>[[.,.],[[.,.],.]] [[1,4],[2],[3]]=>[3,2,1,4]=>[3,1,2,4]=>[[.,[.,.]],[.,.]] [[1,3],[2],[4]]=>[4,2,1,3]=>[3,1,4,2]=>[[.,[.,.]],[.,.]] [[1,2],[3],[4]]=>[4,3,1,2]=>[2,4,1,3]=>[[.,.],[[.,.],.]] [[1],[2],[3],[4]]=>[4,3,2,1]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [[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]=>[[.,.],[.,[.,[.,.]]]] [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]] [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]] [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]] [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]] [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[.,.],[[.,.],[.,.]]] [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]] [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[2,4,3,5,1]=>[[.,.],[[.,.],[.,.]]] [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]] [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]] [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[3,1,4,2,5]=>[[.,[.,.]],[.,[.,.]]] [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[2,4,1,3,5]=>[[.,.],[[.,.],[.,.]]] [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[3,1,4,5,2]=>[[.,[.,.]],[.,[.,.]]] [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[2,4,1,5,3]=>[[.,.],[[.,.],[.,.]]] [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[2,3,5,1,4]=>[[.,.],[.,[[.,.],.]]] [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]] [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]] [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]] [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]] [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[2,5,4,1,3]=>[[.,.],[[[.,.],.],.]] [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]] [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[4,1,2,5,3]=>[[.,[.,[.,.]]],[.,.]] [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[3,1,5,2,4]=>[[.,[.,.]],[[.,.],.]] [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[2,5,1,3,4]=>[[.,.],[[.,[.,.]],.]] [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.] [[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]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[[.,.],[.,[[.,.],[.,.]]]] [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>[[.,.],[.,[[.,.],[.,.]]]] [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]] [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[2,4,1,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[3,1,4,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[2,4,1,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[2,3,5,1,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[3,1,4,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[2,4,1,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[2,3,5,1,6,4]=>[[.,.],[.,[[.,.],[.,.]]]] [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>[[.,.],[.,[.,[[.,.],.]]]] [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]] [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>[[.,.],[[.,[.,.]],[.,.]]] [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]] [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>[[.,.],[[.,.],[[.,.],.]]] [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]] [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]] [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[2,5,4,3,1,6]=>[[.,.],[[[.,.],.],[.,.]]] [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[3,4,5,1,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[2,5,4,1,3,6]=>[[.,.],[[[.,.],.],[.,.]]] [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[2,5,4,3,6,1]=>[[.,.],[[[.,.],.],[.,.]]] [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[3,5,4,6,2,1]=>[[[.,.],.],[[.,.],[.,.]]] [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[2,4,5,6,3,1]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]] [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[3,4,5,1,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[2,5,4,1,6,3]=>[[.,.],[[[.,.],.],[.,.]]] [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[3,5,4,6,1,2]=>[[.,[.,.]],[[.,.],[.,.]]] [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[2,4,5,6,1,3]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>[[.,.],[.,[[[.,.],.],.]]] [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[4,1,2,5,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[3,1,5,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]] [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[2,5,1,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]] [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[4,1,2,5,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[3,1,5,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]] [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]] [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>[[.,[.,.]],[.,[[.,.],.]]] [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>[[.,.],[[.,.],[[.,.],.]]] [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>[[.,.],[.,[[.,[.,.]],.]]] [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[4,5,3,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,5,6,4,1,2]=>[[.,[.,.]],[[.,.],[.,.]]] [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[2,6,5,4,1,3]=>[[.,.],[[[[.,.],.],.],.]] [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[3,4,6,1,5,2]=>[[.,[.,.]],[.,[[.,.],.]]] [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>[[.,.],[[[.,.],[.,.]],.]] [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]] [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[4,5,2,6,3,1]=>[[[.,.],[.,.]],[.,[.,.]]] [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[3,5,6,2,4,1]=>[[[.,.],.],[[.,.],[.,.]]] [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],.]] [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[4,5,2,6,1,3]=>[[[.,.],[.,.]],[.,[.,.]]] [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[3,5,6,2,1,4]=>[[[.,.],.],[[.,.],[.,.]]] [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>[[.,.],[[[.,[.,.]],.],.]] [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[3,4,6,1,2,5]=>[[.,[.,.]],[.,[[.,.],.]]] [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>[[.,.],[[[.,.],[.,.]],.]] [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>[[.,[.,[.,.]]],[[.,.],.]] [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]] [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[2,6,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]] [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.] [[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]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[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]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[3,1,4,5,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[2,4,1,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[2,3,5,1,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[3,1,4,5,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[2,4,1,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[2,3,5,1,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[2,3,4,6,1,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[2,4,1,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[2,3,5,1,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[2,3,4,6,1,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[2,3,4,5,7,1,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[2,5,4,3,1,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[3,4,5,1,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[2,5,4,1,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[2,5,4,3,6,1,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[3,5,4,6,2,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[2,4,5,6,3,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[2,3,6,5,4,1,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[3,4,5,1,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[2,5,4,1,6,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[3,5,4,6,1,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[2,4,5,6,1,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[2,3,6,5,1,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[3,4,5,2,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[2,5,4,3,6,7,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[3,5,4,6,2,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[2,4,5,6,3,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[2,3,6,5,4,7,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[3,6,4,5,7,2,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[2,4,6,5,7,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[2,3,5,6,7,4,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[2,3,4,7,6,5,1]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[3,4,5,1,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[2,5,4,1,6,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[3,5,4,6,1,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[2,4,5,6,1,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[2,3,6,5,1,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[3,6,4,5,7,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[2,4,6,5,7,1,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[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]]=>[7,5,6,1,2,3,4]=>[2,3,4,7,6,1,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[4,1,2,5,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[3,1,5,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[2,5,1,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[4,1,2,5,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[3,1,5,2,6,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[2,5,1,3,6,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[3,1,4,6,2,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[2,4,1,6,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[2,3,6,1,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[4,1,2,5,6,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[3,1,5,2,6,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[2,5,1,3,6,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[3,1,4,6,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[2,4,1,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[2,3,6,1,4,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[3,1,4,5,7,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[2,4,1,5,7,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[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]]=>[7,6,5,1,2,3,4]=>[2,3,4,7,1,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[3,4,6,2,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[2,6,4,3,5,7,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[3,4,6,5,2,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[2,6,4,5,3,7,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[4,3,2,5,7,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[3,4,5,2,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[2,5,4,3,7,6,1]=>[[.,.],[[[.,.],.],[[.,.],.]]] [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[3,5,4,7,2,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]] [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[2,4,5,7,3,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[2,3,7,5,4,6,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[2,5,4,6,7,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[3,5,4,7,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]] [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[2,4,5,7,6,3,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[2,3,7,5,6,4,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[2,5,4,6,7,1,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[3,5,4,7,6,1,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[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]]=>[7,4,5,6,1,2,3]=>[2,3,7,5,6,1,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[3,5,6,4,1,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[2,6,5,4,1,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]] [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[3,4,6,1,5,2,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[2,6,4,1,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[4,5,3,6,1,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[3,5,6,4,1,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[2,6,5,4,1,7,3]=>[[.,.],[[[[.,.],.],.],[.,.]]] [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[3,4,6,1,5,7,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[2,6,4,1,5,7,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[4,6,3,5,7,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[3,6,5,4,7,1,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[2,5,6,4,7,1,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[3,6,4,7,5,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[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],[5,7]]=>[5,7,4,6,1,2,3]=>[2,3,7,6,5,1,4]=>[[.,.],[.,[[[[.,.],.],.],.]]] [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[3,4,5,1,7,6,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[2,5,4,1,7,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[3,5,4,7,1,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[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],[6,7]]=>[6,7,4,5,1,2,3]=>[2,3,7,5,1,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[4,5,2,6,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[3,5,6,2,4,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[2,6,5,3,4,1,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[4,5,2,6,1,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[3,5,6,2,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[2,6,5,3,1,4,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[3,4,6,1,2,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[2,6,4,1,3,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[5,4,2,3,6,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[4,5,2,6,3,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[3,5,6,2,4,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[2,6,5,3,4,7,1]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[4,6,2,5,7,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[3,6,5,2,7,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]] [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[2,5,6,3,7,4,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[3,6,4,7,2,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[2,4,6,7,3,5,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[2,3,7,6,4,5,1]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[4,5,2,6,1,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[3,5,6,2,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[2,6,5,3,1,7,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[3,4,6,1,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[2,6,4,1,3,7,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[4,6,2,5,7,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[3,6,5,2,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]] [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[2,5,6,3,7,1,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[3,6,4,7,2,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[2,4,6,7,3,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[2,3,7,6,4,1,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[3,4,5,1,7,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[2,5,4,1,7,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]] [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[3,5,4,7,1,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[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]]=>[7,6,4,5,1,2,3]=>[2,3,7,5,1,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[5,1,2,3,6,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[4,1,2,6,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[3,1,6,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[2,6,1,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[5,1,2,3,6,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[4,1,2,6,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[3,1,6,2,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[2,6,1,3,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[4,1,2,5,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[3,1,5,2,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[2,5,1,3,7,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[3,1,4,7,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [[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]]=>[7,6,5,4,1,2,3]=>[2,3,7,1,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[4,6,5,7,3,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [[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],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[2,7,6,5,4,1,3]=>[[.,.],[[[[[.,.],.],.],.],.]] [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[4,5,6,7,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[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],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[2,7,5,6,1,4,3]=>[[.,.],[[[[.,.],.],[.,.]],.]] [[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],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[2,7,4,1,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]] [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[3,5,7,6,1,2,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[2,7,5,6,1,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [[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]]=>[7,5,6,3,4,1,2]=>[2,7,4,1,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],.]] [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[6,5,2,3,4,7,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[5,6,2,3,7,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[4,6,2,7,3,5,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[3,6,7,2,4,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[2,7,6,3,4,5,1]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[5,6,2,3,7,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[4,6,2,7,3,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[3,6,7,2,4,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[2,7,6,3,4,1,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[4,5,2,7,1,3,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[3,5,7,2,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]] [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[2,7,5,3,1,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [[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]]=>[7,6,5,3,4,1,2]=>[2,7,4,1,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,7,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[4,1,2,7,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [[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]]=>[7,6,5,4,3,1,2]=>[2,7,1,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [[1,2,3,4,5,6,7,8]]=>[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
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.