Identifier
Mp00081: Standard tableaux reading word permutationPermutations
Mp00061: Permutations to increasing treeBinary trees
Mp00017: Binary trees to 312-avoiding permutationPermutations
Images
=>
Cc0007;cc-rep-0Cc0010;cc-rep-2
[[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]=>[[.,.],[.,.]]=>[1,3,2] [[1,2],[3]]=>[3,1,2]=>[[.,.],[.,.]]=>[1,3,2] [[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]=>[[.,.],[.,[.,.]]]=>[1,4,3,2] [[1,2,4],[3]]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]=>[1,4,3,2] [[1,2,3],[4]]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]=>[1,4,3,2] [[1,3],[2,4]]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]=>[2,1,4,3] [[1,2],[3,4]]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[2,1,4,3] [[1,4],[2],[3]]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[1,2,4,3] [[1,3],[2],[4]]=>[4,2,1,3]=>[[[.,.],.],[.,.]]=>[1,2,4,3] [[1,2],[3],[4]]=>[4,3,1,2]=>[[[.,.],.],[.,.]]=>[1,2,4,3] [[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]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2] [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2] [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2] [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2] [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3] [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3] [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3] [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3] [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3] [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4] [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4] [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4] [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4] [[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]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2] [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2] [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2] [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2] [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2] [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4] [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4] [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4] [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4] [[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]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4] [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5] [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5] [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5] [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5] [[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]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5] [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5] [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5] [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5] [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5] [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5] [[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]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2] [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2] [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2] [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2] [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2] [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2] [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[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]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3] [[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]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5] [[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6] [[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]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7] [[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
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.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.