Identifier
Mp00283: non-nesting-exceedence permutationPermutations
Mp00069: Permutations complementPermutations
Mp00068: Permutations Simion-Schmidt mapPermutations
Mp00060: Permutations Robinson-Schensted tableau shape
Images
=>
Cc0012;cc-rep-0Cc0002;cc-rep-4
[(1,2)]=>[2,1]=>[1,2]=>[1,2]=>[2] [(1,2),(3,4)]=>[2,1,4,3]=>[3,4,1,2]=>[3,4,1,2]=>[2,2] [(1,3),(2,4)]=>[3,4,1,2]=>[2,1,4,3]=>[2,1,4,3]=>[2,2] [(1,4),(2,3)]=>[3,4,2,1]=>[2,1,3,4]=>[2,1,4,3]=>[2,2] [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[2,2,2] [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[4,3,6,5,1,2]=>[2,2,2] [(1,4),(2,3),(5,6)]=>[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>[4,3,6,5,1,2]=>[2,2,2] [(1,5),(2,3),(4,6)]=>[3,5,2,6,1,4]=>[4,2,5,1,6,3]=>[4,2,6,1,5,3]=>[2,2,2] [(1,6),(2,3),(4,5)]=>[3,5,2,6,4,1]=>[4,2,5,1,3,6]=>[4,2,6,1,5,3]=>[2,2,2] [(1,6),(2,4),(3,5)]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>[3,2,1,6,5,4]=>[2,2,2] [(1,5),(2,4),(3,6)]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>[3,2,1,6,5,4]=>[2,2,2] [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[2,2,2] [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[2,2,2] [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[5,6,2,1,4,3]=>[2,2,2] [(1,2),(3,6),(4,5)]=>[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>[5,6,2,1,4,3]=>[2,2,2] [(1,3),(2,6),(4,5)]=>[3,5,1,6,4,2]=>[4,2,6,1,3,5]=>[4,2,6,1,5,3]=>[2,2,2] [(1,4),(2,6),(3,5)]=>[4,5,6,1,3,2]=>[3,2,1,6,4,5]=>[3,2,1,6,5,4]=>[2,2,2] [(1,5),(2,6),(3,4)]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>[3,2,1,6,5,4]=>[2,2,2] [(1,6),(2,5),(3,4)]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[3,2,1,6,5,4]=>[2,2,2] [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2] [(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[6,5,8,7,3,4,1,2]=>[6,5,8,7,3,4,1,2]=>[2,2,2,2] [(1,4),(2,3),(5,6),(7,8)]=>[3,4,2,1,6,5,8,7]=>[6,5,7,8,3,4,1,2]=>[6,5,8,7,3,4,1,2]=>[2,2,2,2] [(1,5),(2,3),(4,6),(7,8)]=>[3,5,2,6,1,4,8,7]=>[6,4,7,3,8,5,1,2]=>[6,4,8,3,7,5,1,2]=>[2,2,2,2] [(1,6),(2,3),(4,5),(7,8)]=>[3,5,2,6,4,1,8,7]=>[6,4,7,3,5,8,1,2]=>[6,4,8,3,7,5,1,2]=>[2,2,2,2] [(1,7),(2,3),(4,5),(6,8)]=>[3,5,2,7,4,8,1,6]=>[6,4,7,2,5,1,8,3]=>[6,4,8,2,7,1,5,3]=>[2,2,2,2] [(1,8),(2,3),(4,5),(6,7)]=>[3,5,2,7,4,8,6,1]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[2,2,2,2] [(1,8),(2,4),(3,5),(6,7)]=>[4,5,7,2,3,8,6,1]=>[5,4,2,7,6,1,3,8]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,7),(2,4),(3,5),(6,8)]=>[4,5,7,2,3,8,1,6]=>[5,4,2,7,6,1,8,3]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,6),(2,4),(3,5),(7,8)]=>[4,5,6,2,3,1,8,7]=>[5,4,3,7,6,8,1,2]=>[5,4,3,8,7,6,1,2]=>[2,2,2,2] [(1,5),(2,4),(3,6),(7,8)]=>[4,5,6,2,1,3,8,7]=>[5,4,3,7,8,6,1,2]=>[5,4,3,8,7,6,1,2]=>[2,2,2,2] [(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[5,4,3,8,7,6,1,2]=>[5,4,3,8,7,6,1,2]=>[2,2,2,2] [(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[6,4,8,3,7,5,1,2]=>[6,4,8,3,7,5,1,2]=>[2,2,2,2] [(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[2,2,2,2] [(1,2),(3,6),(4,5),(7,8)]=>[2,1,5,6,4,3,8,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[2,2,2,2] [(1,3),(2,6),(4,5),(7,8)]=>[3,5,1,6,4,2,8,7]=>[6,4,8,3,5,7,1,2]=>[6,4,8,3,7,5,1,2]=>[2,2,2,2] [(1,4),(2,6),(3,5),(7,8)]=>[4,5,6,1,3,2,8,7]=>[5,4,3,8,6,7,1,2]=>[5,4,3,8,7,6,1,2]=>[2,2,2,2] [(1,5),(2,6),(3,4),(7,8)]=>[4,5,6,3,1,2,8,7]=>[5,4,3,6,8,7,1,2]=>[5,4,3,8,7,6,1,2]=>[2,2,2,2] [(1,6),(2,5),(3,4),(7,8)]=>[4,5,6,3,2,1,8,7]=>[5,4,3,6,7,8,1,2]=>[5,4,3,8,7,6,1,2]=>[2,2,2,2] [(1,7),(2,5),(3,4),(6,8)]=>[4,5,7,3,2,8,1,6]=>[5,4,2,6,7,1,8,3]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,8),(2,5),(3,4),(6,7)]=>[4,5,7,3,2,8,6,1]=>[5,4,2,6,7,1,3,8]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,8),(2,6),(3,4),(5,7)]=>[4,6,7,3,8,2,5,1]=>[5,3,2,6,1,7,4,8]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,7),(2,6),(3,4),(5,8)]=>[4,6,7,3,8,2,1,5]=>[5,3,2,6,1,7,8,4]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,6),(2,7),(3,4),(5,8)]=>[4,6,7,3,8,1,2,5]=>[5,3,2,6,1,8,7,4]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,5),(2,7),(3,4),(6,8)]=>[4,5,7,3,1,8,2,6]=>[5,4,2,6,8,1,7,3]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,4),(2,7),(3,5),(6,8)]=>[4,5,7,1,3,8,2,6]=>[5,4,2,8,6,1,7,3]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,3),(2,7),(4,5),(6,8)]=>[3,5,1,7,4,8,2,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[2,2,2,2] [(1,2),(3,7),(4,5),(6,8)]=>[2,1,5,7,4,8,3,6]=>[7,8,4,2,5,1,6,3]=>[7,8,4,2,6,1,5,3]=>[2,2,2,2] [(1,2),(3,8),(4,5),(6,7)]=>[2,1,5,7,4,8,6,3]=>[7,8,4,2,5,1,3,6]=>[7,8,4,2,6,1,5,3]=>[2,2,2,2] [(1,3),(2,8),(4,5),(6,7)]=>[3,5,1,7,4,8,6,2]=>[6,4,8,2,5,1,3,7]=>[6,4,8,2,7,1,5,3]=>[2,2,2,2] [(1,4),(2,8),(3,5),(6,7)]=>[4,5,7,1,3,8,6,2]=>[5,4,2,8,6,1,3,7]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,5),(2,8),(3,4),(6,7)]=>[4,5,7,3,1,8,6,2]=>[5,4,2,6,8,1,3,7]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,6),(2,8),(3,4),(5,7)]=>[4,6,7,3,8,1,5,2]=>[5,3,2,6,1,8,4,7]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,7),(2,8),(3,4),(5,6)]=>[4,6,7,3,8,5,1,2]=>[5,3,2,6,1,4,8,7]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,8),(2,7),(3,4),(5,6)]=>[4,6,7,3,8,5,2,1]=>[5,3,2,6,1,4,7,8]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,8),(2,7),(3,5),(4,6)]=>[5,6,7,8,3,4,2,1]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,7),(2,8),(3,5),(4,6)]=>[5,6,7,8,3,4,1,2]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,6),(2,8),(3,5),(4,7)]=>[5,6,7,8,3,1,4,2]=>[4,3,2,1,6,8,5,7]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,5),(2,8),(3,6),(4,7)]=>[5,6,7,8,1,3,4,2]=>[4,3,2,1,8,6,5,7]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,4),(2,8),(3,6),(5,7)]=>[4,6,7,1,8,3,5,2]=>[5,3,2,8,1,6,4,7]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,3),(2,8),(4,6),(5,7)]=>[3,6,1,7,8,4,5,2]=>[6,3,8,2,1,5,4,7]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,2),(3,8),(4,6),(5,7)]=>[2,1,6,7,8,4,5,3]=>[7,8,3,2,1,5,4,6]=>[7,8,3,2,1,6,5,4]=>[2,2,2,2] [(1,2),(3,7),(4,6),(5,8)]=>[2,1,6,7,8,4,3,5]=>[7,8,3,2,1,5,6,4]=>[7,8,3,2,1,6,5,4]=>[2,2,2,2] [(1,3),(2,7),(4,6),(5,8)]=>[3,6,1,7,8,4,2,5]=>[6,3,8,2,1,5,7,4]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,4),(2,7),(3,6),(5,8)]=>[4,6,7,1,8,3,2,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,5),(2,7),(3,6),(4,8)]=>[5,6,7,8,1,3,2,4]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,6),(2,7),(3,5),(4,8)]=>[5,6,7,8,3,1,2,4]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,7),(2,6),(3,5),(4,8)]=>[5,6,7,8,3,2,1,4]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,8),(2,6),(3,5),(4,7)]=>[5,6,7,8,3,2,4,1]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,8),(2,5),(3,6),(4,7)]=>[5,6,7,8,2,3,4,1]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,7),(2,5),(3,6),(4,8)]=>[5,6,7,8,2,3,1,4]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,6),(2,5),(3,7),(4,8)]=>[5,6,7,8,2,1,3,4]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[6,3,8,2,1,7,5,4]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[7,8,3,2,1,6,5,4]=>[7,8,3,2,1,6,5,4]=>[2,2,2,2] [(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[7,8,4,2,6,1,5,3]=>[7,8,4,2,6,1,5,3]=>[2,2,2,2] [(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[2,2,2,2] [(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[5,4,2,8,7,1,6,3]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,5),(2,4),(3,7),(6,8)]=>[4,5,7,2,1,8,3,6]=>[5,4,2,7,8,1,6,3]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,6),(2,4),(3,7),(5,8)]=>[4,6,7,2,8,1,3,5]=>[5,3,2,7,1,8,6,4]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,7),(2,4),(3,6),(5,8)]=>[4,6,7,2,8,3,1,5]=>[5,3,2,7,1,6,8,4]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,8),(2,4),(3,6),(5,7)]=>[4,6,7,2,8,3,5,1]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,8),(2,3),(4,6),(5,7)]=>[3,6,2,7,8,4,5,1]=>[6,3,7,2,1,5,4,8]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,7),(2,3),(4,6),(5,8)]=>[3,6,2,7,8,4,1,5]=>[6,3,7,2,1,5,8,4]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,6),(2,3),(4,7),(5,8)]=>[3,6,2,7,8,1,4,5]=>[6,3,7,2,1,8,5,4]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,5),(2,3),(4,7),(6,8)]=>[3,5,2,7,1,8,4,6]=>[6,4,7,2,8,1,5,3]=>[6,4,8,2,7,1,5,3]=>[2,2,2,2] [(1,4),(2,3),(5,7),(6,8)]=>[3,4,2,1,7,8,5,6]=>[6,5,7,8,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[2,2,2,2] [(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[2,2,2,2] [(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[7,8,5,6,2,1,4,3]=>[7,8,5,6,2,1,4,3]=>[2,2,2,2] [(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,7,8,6,5]=>[7,8,5,6,2,1,3,4]=>[7,8,5,6,2,1,4,3]=>[2,2,2,2] [(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,7,8,6,5]=>[6,5,8,7,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[2,2,2,2] [(1,4),(2,3),(5,8),(6,7)]=>[3,4,2,1,7,8,6,5]=>[6,5,7,8,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[2,2,2,2] [(1,5),(2,3),(4,8),(6,7)]=>[3,5,2,7,1,8,6,4]=>[6,4,7,2,8,1,3,5]=>[6,4,8,2,7,1,5,3]=>[2,2,2,2] [(1,6),(2,3),(4,8),(5,7)]=>[3,6,2,7,8,1,5,4]=>[6,3,7,2,1,8,4,5]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,7),(2,3),(4,8),(5,6)]=>[3,6,2,7,8,5,1,4]=>[6,3,7,2,1,4,8,5]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,8),(2,3),(4,7),(5,6)]=>[3,6,2,7,8,5,4,1]=>[6,3,7,2,1,4,5,8]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,8),(2,4),(3,7),(5,6)]=>[4,6,7,2,8,5,3,1]=>[5,3,2,7,1,4,6,8]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,7),(2,4),(3,8),(5,6)]=>[4,6,7,2,8,5,1,3]=>[5,3,2,7,1,4,8,6]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,6),(2,4),(3,8),(5,7)]=>[4,6,7,2,8,1,5,3]=>[5,3,2,7,1,8,4,6]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,5),(2,4),(3,8),(6,7)]=>[4,5,7,2,1,8,6,3]=>[5,4,2,7,8,1,3,6]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,4),(2,5),(3,8),(6,7)]=>[4,5,7,1,2,8,6,3]=>[5,4,2,8,7,1,3,6]=>[5,4,2,8,7,1,6,3]=>[2,2,2,2] [(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,7,2,8,6,4]=>[6,4,8,2,7,1,3,5]=>[6,4,8,2,7,1,5,3]=>[2,2,2,2] [(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,7,3,8,6,4]=>[7,8,4,2,6,1,3,5]=>[7,8,4,2,6,1,5,3]=>[2,2,2,2] [(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,7,8,3,5,4]=>[7,8,3,2,1,6,4,5]=>[7,8,3,2,1,6,5,4]=>[2,2,2,2] [(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,7,8,2,5,4]=>[6,3,8,2,1,7,4,5]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,4),(2,6),(3,8),(5,7)]=>[4,6,7,1,8,2,5,3]=>[5,3,2,8,1,7,4,6]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,5),(2,6),(3,8),(4,7)]=>[5,6,7,8,1,2,4,3]=>[4,3,2,1,8,7,5,6]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,6),(2,5),(3,8),(4,7)]=>[5,6,7,8,2,1,4,3]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,7),(2,5),(3,8),(4,6)]=>[5,6,7,8,2,4,1,3]=>[4,3,2,1,7,5,8,6]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,8),(2,5),(3,7),(4,6)]=>[5,6,7,8,2,4,3,1]=>[4,3,2,1,7,5,6,8]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,8),(2,6),(3,7),(4,5)]=>[5,6,7,8,4,2,3,1]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,7),(2,6),(3,8),(4,5)]=>[5,6,7,8,4,2,1,3]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,6),(2,7),(3,8),(4,5)]=>[5,6,7,8,4,1,2,3]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,5),(2,7),(3,8),(4,6)]=>[5,6,7,8,1,4,2,3]=>[4,3,2,1,8,5,7,6]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,4),(2,7),(3,8),(5,6)]=>[4,6,7,1,8,5,2,3]=>[5,3,2,8,1,4,7,6]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,3),(2,7),(4,8),(5,6)]=>[3,6,1,7,8,5,2,4]=>[6,3,8,2,1,4,7,5]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,2),(3,7),(4,8),(5,6)]=>[2,1,6,7,8,5,3,4]=>[7,8,3,2,1,4,6,5]=>[7,8,3,2,1,6,5,4]=>[2,2,2,2] [(1,2),(3,8),(4,7),(5,6)]=>[2,1,6,7,8,5,4,3]=>[7,8,3,2,1,4,5,6]=>[7,8,3,2,1,6,5,4]=>[2,2,2,2] [(1,3),(2,8),(4,7),(5,6)]=>[3,6,1,7,8,5,4,2]=>[6,3,8,2,1,4,5,7]=>[6,3,8,2,1,7,5,4]=>[2,2,2,2] [(1,4),(2,8),(3,7),(5,6)]=>[4,6,7,1,8,5,3,2]=>[5,3,2,8,1,4,6,7]=>[5,3,2,8,1,7,6,4]=>[2,2,2,2] [(1,5),(2,8),(3,7),(4,6)]=>[5,6,7,8,1,4,3,2]=>[4,3,2,1,8,5,6,7]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,6),(2,8),(3,7),(4,5)]=>[5,6,7,8,4,1,3,2]=>[4,3,2,1,5,8,6,7]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,7),(2,8),(3,6),(4,5)]=>[5,6,7,8,4,3,1,2]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,8),(2,7),(3,6),(4,5)]=>[5,6,7,8,4,3,2,1]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [(1,6),(2,7),(3,8),(4,9),(5,10)]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[5,4,3,2,1,10,9,8,7,6]=>[2,2,2,2,2] [(1,10),(2,6),(3,7),(4,8),(5,9)]=>[6,7,8,9,10,2,3,4,5,1]=>[5,4,3,2,1,9,8,7,6,10]=>[5,4,3,2,1,10,9,8,7,6]=>[2,2,2,2,2] [(1,10),(2,9),(3,8),(4,7),(5,6)]=>[6,7,8,9,10,5,4,3,2,1]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,10,9,8,7,6]=>[2,2,2,2,2] [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>[6,5,4,3,2,1,7,8,9,10,11,12]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[2,2,2,2,2,2] [(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[2,2,2,2,2,2]
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
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 the shape of its corresponding insertion and recording tableau.