Identifier
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ 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
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.