Identifier
Mp00058: to permutationPermutations
Mp00059: Permutations Robinson-Schensted insertion tableau
Images
=>
Cc0012;cc-rep-0Cc0007;cc-rep-2
[(1,2)]=>[2,1]=>[[1],[2]] [(1,2),(3,4)]=>[2,1,4,3]=>[[1,3],[2,4]] [(1,3),(2,4)]=>[3,4,1,2]=>[[1,2],[3,4]] [(1,4),(2,3)]=>[4,3,2,1]=>[[1],[2],[3],[4]] [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]] [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[[1,2,5],[3,4,6]] [(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[[1,5],[2,6],[3],[4]] [(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>[[1,4],[2,6],[3],[5]] [(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[[1,4],[2,5],[3],[6]] [(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6]] [(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>[[1,3],[2,6],[4],[5]] [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[[1,2,3],[4,5,6]] [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[[1,2,4],[3,5,6]] [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[[1,3,4],[2,5,6]] [(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[[1,3],[2,4],[5],[6]] [(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>[[1,2],[3,4],[5],[6]] [(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>[[1,2],[3,5],[4],[6]] [(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5]] [(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]] [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]] [(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]] [(1,4),(2,3),(5,6),(7,8)]=>[4,3,2,1,6,5,8,7]=>[[1,5,7],[2,6,8],[3],[4]] [(1,5),(2,3),(4,6),(7,8)]=>[5,3,2,6,1,4,8,7]=>[[1,4,7],[2,6,8],[3],[5]] [(1,6),(2,3),(4,5),(7,8)]=>[6,3,2,5,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]] [(1,7),(2,3),(4,5),(6,8)]=>[7,3,2,5,4,8,1,6]=>[[1,4,6],[2,5,8],[3],[7]] [(1,8),(2,3),(4,5),(6,7)]=>[8,3,2,5,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]] [(1,8),(2,4),(3,5),(6,7)]=>[8,4,5,2,3,7,6,1]=>[[1,3,6],[2,5,7],[4],[8]] [(1,7),(2,4),(3,5),(6,8)]=>[7,4,5,2,3,8,1,6]=>[[1,3,6],[2,5,8],[4],[7]] [(1,6),(2,4),(3,5),(7,8)]=>[6,4,5,2,3,1,8,7]=>[[1,3,7],[2,5,8],[4],[6]] [(1,5),(2,4),(3,6),(7,8)]=>[5,4,6,2,1,3,8,7]=>[[1,3,7],[2,6,8],[4],[5]] [(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]] [(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]] [(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]] [(1,2),(3,6),(4,5),(7,8)]=>[2,1,6,5,4,3,8,7]=>[[1,3,7],[2,4,8],[5],[6]] [(1,3),(2,6),(4,5),(7,8)]=>[3,6,1,5,4,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]] [(1,4),(2,6),(3,5),(7,8)]=>[4,6,5,1,3,2,8,7]=>[[1,2,7],[3,5,8],[4],[6]] [(1,5),(2,6),(3,4),(7,8)]=>[5,6,4,3,1,2,8,7]=>[[1,2,7],[3,6,8],[4],[5]] [(1,6),(2,5),(3,4),(7,8)]=>[6,5,4,3,2,1,8,7]=>[[1,7],[2,8],[3],[4],[5],[6]] [(1,7),(2,5),(3,4),(6,8)]=>[7,5,4,3,2,8,1,6]=>[[1,6],[2,8],[3],[4],[5],[7]] [(1,8),(2,5),(3,4),(6,7)]=>[8,5,4,3,2,7,6,1]=>[[1,6],[2,7],[3],[4],[5],[8]] [(1,8),(2,6),(3,4),(5,7)]=>[8,6,4,3,7,2,5,1]=>[[1,5],[2,7],[3],[4],[6],[8]] [(1,7),(2,6),(3,4),(5,8)]=>[7,6,4,3,8,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]] [(1,6),(2,7),(3,4),(5,8)]=>[6,7,4,3,8,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]] [(1,5),(2,7),(3,4),(6,8)]=>[5,7,4,3,1,8,2,6]=>[[1,2,6],[3,7,8],[4],[5]] [(1,4),(2,7),(3,5),(6,8)]=>[4,7,5,1,3,8,2,6]=>[[1,2,6],[3,5,8],[4],[7]] [(1,3),(2,7),(4,5),(6,8)]=>[3,7,1,5,4,8,2,6]=>[[1,2,6],[3,4,8],[5],[7]] [(1,2),(3,7),(4,5),(6,8)]=>[2,1,7,5,4,8,3,6]=>[[1,3,6],[2,4,8],[5],[7]] [(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]] [(1,3),(2,8),(4,5),(6,7)]=>[3,8,1,5,4,7,6,2]=>[[1,2,6],[3,4,7],[5],[8]] [(1,4),(2,8),(3,5),(6,7)]=>[4,8,5,1,3,7,6,2]=>[[1,2,6],[3,5,7],[4],[8]] [(1,5),(2,8),(3,4),(6,7)]=>[5,8,4,3,1,7,6,2]=>[[1,2],[3,6],[4,7],[5,8]] [(1,6),(2,8),(3,4),(5,7)]=>[6,8,4,3,7,1,5,2]=>[[1,2],[3,5],[4,7],[6,8]] [(1,7),(2,8),(3,4),(5,6)]=>[7,8,4,3,6,5,1,2]=>[[1,2],[3,5],[4,6],[7,8]] [(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]] [(1,8),(2,7),(3,5),(4,6)]=>[8,7,5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]] [(1,7),(2,8),(3,5),(4,6)]=>[7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]] [(1,6),(2,8),(3,5),(4,7)]=>[6,8,5,7,3,1,4,2]=>[[1,2],[3,4],[5,7],[6,8]] [(1,5),(2,8),(3,6),(4,7)]=>[5,8,6,7,1,3,4,2]=>[[1,2,4],[3,6,7],[5],[8]] [(1,4),(2,8),(3,6),(5,7)]=>[4,8,6,1,7,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]] [(1,3),(2,8),(4,6),(5,7)]=>[3,8,1,6,7,4,5,2]=>[[1,2,5],[3,4,7],[6],[8]] [(1,2),(3,8),(4,6),(5,7)]=>[2,1,8,6,7,4,5,3]=>[[1,3,5],[2,4,7],[6],[8]] [(1,2),(3,7),(4,6),(5,8)]=>[2,1,7,6,8,4,3,5]=>[[1,3,5],[2,4,8],[6],[7]] [(1,3),(2,7),(4,6),(5,8)]=>[3,7,1,6,8,4,2,5]=>[[1,2,5],[3,4,8],[6],[7]] [(1,4),(2,7),(3,6),(5,8)]=>[4,7,6,1,8,3,2,5]=>[[1,2,5],[3,6,8],[4],[7]] [(1,5),(2,7),(3,6),(4,8)]=>[5,7,6,8,1,3,2,4]=>[[1,2,4],[3,6,8],[5],[7]] [(1,6),(2,7),(3,5),(4,8)]=>[6,7,5,8,3,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]] [(1,7),(2,6),(3,5),(4,8)]=>[7,6,5,8,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]] [(1,8),(2,6),(3,5),(4,7)]=>[8,6,5,7,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]] [(1,8),(2,5),(3,6),(4,7)]=>[8,5,6,7,2,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]] [(1,7),(2,5),(3,6),(4,8)]=>[7,5,6,8,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]] [(1,6),(2,5),(3,7),(4,8)]=>[6,5,7,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]] [(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]] [(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]] [(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[[1,2,4,5],[3,6,7,8]] [(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]] [(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[[1,3,4,6],[2,5,7,8]] [(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[[1,2,4,6],[3,5,7,8]] [(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]] [(1,5),(2,4),(3,7),(6,8)]=>[5,4,7,2,1,8,3,6]=>[[1,3,6],[2,7,8],[4],[5]] [(1,6),(2,4),(3,7),(5,8)]=>[6,4,7,2,8,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]] [(1,7),(2,4),(3,6),(5,8)]=>[7,4,6,2,8,3,1,5]=>[[1,3,5],[2,6,8],[4],[7]] [(1,8),(2,4),(3,6),(5,7)]=>[8,4,6,2,7,3,5,1]=>[[1,3,5],[2,6,7],[4],[8]] [(1,8),(2,3),(4,6),(5,7)]=>[8,3,2,6,7,4,5,1]=>[[1,4,5],[2,6,7],[3],[8]] [(1,7),(2,3),(4,6),(5,8)]=>[7,3,2,6,8,4,1,5]=>[[1,4,5],[2,6,8],[3],[7]] [(1,6),(2,3),(4,7),(5,8)]=>[6,3,2,7,8,1,4,5]=>[[1,4,5],[2,7,8],[3],[6]] [(1,5),(2,3),(4,7),(6,8)]=>[5,3,2,7,1,8,4,6]=>[[1,4,6],[2,7,8],[3],[5]] [(1,4),(2,3),(5,7),(6,8)]=>[4,3,2,1,7,8,5,6]=>[[1,5,6],[2,7,8],[3],[4]] [(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]] [(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]] [(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]] [(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,8,7,6,5]=>[[1,2,5],[3,4,6],[7],[8]] [(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8]] [(1,5),(2,3),(4,8),(6,7)]=>[5,3,2,8,1,7,6,4]=>[[1,4],[2,6],[3,7],[5,8]] [(1,6),(2,3),(4,8),(5,7)]=>[6,3,2,8,7,1,5,4]=>[[1,4],[2,5],[3,7],[6,8]] [(1,7),(2,3),(4,8),(5,6)]=>[7,3,2,8,6,5,1,4]=>[[1,4],[2,5],[3,6],[7,8]] [(1,8),(2,3),(4,7),(5,6)]=>[8,3,2,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]] [(1,8),(2,4),(3,7),(5,6)]=>[8,4,7,2,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]] [(1,7),(2,4),(3,8),(5,6)]=>[7,4,8,2,6,5,1,3]=>[[1,3],[2,5],[4,6],[7,8]] [(1,6),(2,4),(3,8),(5,7)]=>[6,4,8,2,7,1,5,3]=>[[1,3],[2,5],[4,7],[6,8]] [(1,5),(2,4),(3,8),(6,7)]=>[5,4,8,2,1,7,6,3]=>[[1,3],[2,6],[4,7],[5,8]] [(1,4),(2,5),(3,8),(6,7)]=>[4,5,8,1,2,7,6,3]=>[[1,2,3],[4,5,6],[7],[8]] [(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,8,2,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]] [(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,8,3,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]] [(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,8,7,3,5,4]=>[[1,3,4],[2,5,7],[6],[8]] [(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,8,7,2,5,4]=>[[1,2,4],[3,5,7],[6],[8]] [(1,4),(2,6),(3,8),(5,7)]=>[4,6,8,1,7,2,5,3]=>[[1,2,3],[4,5,7],[6],[8]] [(1,5),(2,6),(3,8),(4,7)]=>[5,6,8,7,1,2,4,3]=>[[1,2,3],[4,6,7],[5],[8]] [(1,6),(2,5),(3,8),(4,7)]=>[6,5,8,7,2,1,4,3]=>[[1,3],[2,4],[5,7],[6,8]] [(1,7),(2,5),(3,8),(4,6)]=>[7,5,8,6,2,4,1,3]=>[[1,3],[2,4],[5,6],[7,8]] [(1,8),(2,5),(3,7),(4,6)]=>[8,5,7,6,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]] [(1,8),(2,6),(3,7),(4,5)]=>[8,6,7,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]] [(1,7),(2,6),(3,8),(4,5)]=>[7,6,8,5,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]] [(1,6),(2,7),(3,8),(4,5)]=>[6,7,8,5,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]] [(1,5),(2,7),(3,8),(4,6)]=>[5,7,8,6,1,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]] [(1,4),(2,7),(3,8),(5,6)]=>[4,7,8,1,6,5,2,3]=>[[1,2,3],[4,5,8],[6],[7]] [(1,3),(2,7),(4,8),(5,6)]=>[3,7,1,8,6,5,2,4]=>[[1,2,4],[3,5,8],[6],[7]] [(1,2),(3,7),(4,8),(5,6)]=>[2,1,7,8,6,5,3,4]=>[[1,3,4],[2,5,8],[6],[7]] [(1,2),(3,8),(4,7),(5,6)]=>[2,1,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]] [(1,3),(2,8),(4,7),(5,6)]=>[3,8,1,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]] [(1,4),(2,8),(3,7),(5,6)]=>[4,8,7,1,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]] [(1,5),(2,8),(3,7),(4,6)]=>[5,8,7,6,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]] [(1,6),(2,8),(3,7),(4,5)]=>[6,8,7,5,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]] [(1,7),(2,8),(3,6),(4,5)]=>[7,8,6,5,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]] [(1,8),(2,7),(3,6),(4,5)]=>[8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]] [(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]] [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.