Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00064: Permutations —reverse⟶ 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]=>[2,1]=>[[.,.],.]
[[1],[2]]=>[2,1]=>[1,2]=>[.,[.,.]]
[[1,2,3]]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.]
[[1,3],[2]]=>[2,1,3]=>[3,1,2]=>[[.,[.,.]],.]
[[1,2],[3]]=>[3,1,2]=>[2,1,3]=>[[.,.],[.,.]]
[[1],[2],[3]]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,2,3,4]]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[[1,3,4],[2]]=>[2,1,3,4]=>[4,3,1,2]=>[[[.,[.,.]],.],.]
[[1,2,4],[3]]=>[3,1,2,4]=>[4,2,1,3]=>[[[.,.],[.,.]],.]
[[1,2,3],[4]]=>[4,1,2,3]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[[1,3],[2,4]]=>[2,4,1,3]=>[3,1,4,2]=>[[.,[.,.]],[.,.]]
[[1,2],[3,4]]=>[3,4,1,2]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[[1,4],[2],[3]]=>[3,2,1,4]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[[1,3],[2],[4]]=>[4,2,1,3]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]
[[1,2],[3],[4]]=>[4,3,1,2]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1],[2],[3],[4]]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.]
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.]
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[5,3,1,4,2]=>[[[.,[.,.]],[.,.]],.]
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[[[.,.],[[.,.],.]],.]
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[4,3,1,5,2]=>[[[.,[.,.]],.],[.,.]]
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[4,2,1,5,3]=>[[[.,.],[.,.]],[.,.]]
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.]
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]]
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,1,5,2,3]=>[[.,[.,[.,.]]],[.,.]]
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[3,1,5,2,4]=>[[.,[.,.]],[[.,.],.]]
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>[[.,.],[[.,[.,.]],.]]
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[3,1,4,2,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.]
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.]
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.]
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[6,5,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],.]
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],.]
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[6,4,3,1,5,2]=>[[[[.,[.,.]],.],[.,.]],.]
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[6,4,2,1,5,3]=>[[[[.,.],[.,.]],[.,.]],.]
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],.]
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[5,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[.,.]]
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[5,4,2,1,6,3]=>[[[[.,.],[.,.]],.],[.,.]]
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[5,3,2,1,6,4]=>[[[[.,.],.],[.,.]],[.,.]]
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.]
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.]
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.]
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.]
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.]
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]]
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]]
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]]
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>[[[.,.],[[.,.],.]],[.,.]]
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[6,4,1,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[6,3,1,5,2,4]=>[[[.,[.,.]],[[.,.],.]],.]
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],.]
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[6,3,1,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],.]
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],.]
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[5,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[5,3,1,6,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[5,2,1,6,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[4,3,1,6,2,5]=>[[[.,[.,.]],.],[[.,.],.]]
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[4,2,1,6,3,5]=>[[[.,.],[.,.]],[[.,.],.]]
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,[.,.]],.]]
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[5,3,1,4,2,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[.,.]]
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[4,3,1,5,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[4,2,1,5,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.]
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.]
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]]
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[2,1,5,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[3,1,4,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[5,1,6,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[4,1,6,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[3,1,6,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[4,1,5,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[3,1,5,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[3,1,4,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]
[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.]
[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.]
[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.]
[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.]
[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[7,6,5,3,1,4,2]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[[[[[.,.],[[.,.],.]],.],.],.]
[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[7,6,4,3,1,5,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>[[[[[.,.],.],[[.,.],.]],.],.]
[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[7,5,4,3,1,6,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[7,5,4,2,1,6,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[7,5,3,2,1,6,4]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[[[[[.,.],.],.],[[.,.],.]],.]
[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[6,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[6,5,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[6,5,3,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[7,5,3,1,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[7,5,2,1,6,4,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[7,4,2,1,6,5,3]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.]
[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[6,5,3,1,7,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[6,5,2,1,7,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[6,4,3,1,7,5,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[6,3,2,1,7,5,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[5,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[5,4,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[5,3,2,1,7,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[7,6,4,1,5,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[7,6,3,1,5,2,4]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[7,6,3,1,4,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[7,5,4,1,6,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[7,5,3,1,6,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[7,5,2,1,6,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[7,4,3,1,6,2,5]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[7,4,2,1,6,3,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[7,5,3,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[7,4,3,1,5,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[7,4,2,1,5,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[6,5,4,1,7,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[6,5,2,1,7,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[6,4,3,1,7,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[6,4,2,1,7,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[5,4,3,1,7,2,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[5,4,2,1,7,3,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[5,3,2,1,7,4,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[5,4,3,1,6,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[5,4,2,1,6,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[6,4,1,7,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[6,3,1,7,5,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[6,2,1,7,5,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[6,3,1,7,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[6,2,1,7,4,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[5,4,1,7,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[5,3,1,7,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[5,2,1,7,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[4,3,1,7,6,2,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[4,2,1,7,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[5,3,1,7,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[5,2,1,7,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[4,3,1,7,5,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[4,2,1,7,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[5,2,1,6,4,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[4,3,1,6,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[4,2,1,6,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[7,4,1,5,2,6,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[7,2,1,5,3,6,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[7,3,1,4,2,6,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[6,4,1,5,2,7,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[6,3,1,5,2,7,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[6,2,1,4,3,7,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[5,4,1,6,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[7,5,1,6,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[7,4,1,6,2,3,5]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[7,3,1,6,2,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[7,4,1,5,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[7,3,1,5,2,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[7,3,1,4,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[6,5,1,7,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[6,4,1,7,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[6,3,1,7,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[6,2,1,7,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[5,4,1,7,2,3,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[5,3,1,7,2,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[5,2,1,7,3,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[4,3,1,7,2,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[4,2,1,7,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[6,3,1,5,2,4,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[6,3,1,4,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[4,2,1,6,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[4,3,1,5,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[5,1,6,2,7,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[4,1,6,2,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[3,1,6,2,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[2,1,6,3,7,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[4,1,5,2,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[2,1,5,3,7,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[3,1,4,2,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[3,1,5,2,6,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[2,1,5,3,6,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[5,1,7,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[4,1,7,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[3,1,7,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[4,1,6,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[4,1,5,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[3,1,5,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[5,4,1,8,7,2,3,6]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[6,1,8,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[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
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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.
searching the database
Sorry, this map was not found in the database.