Identifier
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
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 $\tau(i) = \sigma(n+1-i)$.
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.