Identifier
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
=>
Cc0012;cc-rep-0Cc0002;cc-rep-2
[(1,2)]=>[2,1]=>[1,1] [(1,2),(3,4)]=>[2,1,4,3]=>[2,2] [(1,3),(2,4)]=>[3,4,1,2]=>[2,2] [(1,4),(2,3)]=>[3,4,2,1]=>[2,1,1] [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[3,3] [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[3,3] [(1,4),(2,3),(5,6)]=>[3,4,2,1,6,5]=>[3,2,1] [(1,5),(2,3),(4,6)]=>[3,5,2,6,1,4]=>[3,2,1] [(1,6),(2,3),(4,5)]=>[3,5,2,6,4,1]=>[3,2,1] [(1,6),(2,4),(3,5)]=>[4,5,6,2,3,1]=>[3,2,1] [(1,5),(2,4),(3,6)]=>[4,5,6,2,1,3]=>[3,2,1] [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[3,3] [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[3,3] [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[3,3] [(1,2),(3,6),(4,5)]=>[2,1,5,6,4,3]=>[3,2,1] [(1,3),(2,6),(4,5)]=>[3,5,1,6,4,2]=>[3,2,1] [(1,4),(2,6),(3,5)]=>[4,5,6,1,3,2]=>[3,2,1] [(1,5),(2,6),(3,4)]=>[4,5,6,3,1,2]=>[3,2,1] [(1,6),(2,5),(3,4)]=>[4,5,6,3,2,1]=>[3,1,1,1] [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[4,4] [(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[4,4] [(1,4),(2,3),(5,6),(7,8)]=>[3,4,2,1,6,5,8,7]=>[4,3,1] [(1,5),(2,3),(4,6),(7,8)]=>[3,5,2,6,1,4,8,7]=>[4,3,1] [(1,6),(2,3),(4,5),(7,8)]=>[3,5,2,6,4,1,8,7]=>[4,3,1] [(1,7),(2,3),(4,5),(6,8)]=>[3,5,2,7,4,8,1,6]=>[4,3,1] [(1,8),(2,3),(4,5),(6,7)]=>[3,5,2,7,4,8,6,1]=>[4,3,1] [(1,8),(2,4),(3,5),(6,7)]=>[4,5,7,2,3,8,6,1]=>[4,3,1] [(1,7),(2,4),(3,5),(6,8)]=>[4,5,7,2,3,8,1,6]=>[4,3,1] [(1,6),(2,4),(3,5),(7,8)]=>[4,5,6,2,3,1,8,7]=>[4,3,1] [(1,5),(2,4),(3,6),(7,8)]=>[4,5,6,2,1,3,8,7]=>[4,3,1] [(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[4,4] [(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[4,4] [(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[4,4] [(1,2),(3,6),(4,5),(7,8)]=>[2,1,5,6,4,3,8,7]=>[4,3,1] [(1,3),(2,6),(4,5),(7,8)]=>[3,5,1,6,4,2,8,7]=>[4,3,1] [(1,4),(2,6),(3,5),(7,8)]=>[4,5,6,1,3,2,8,7]=>[4,3,1] [(1,5),(2,6),(3,4),(7,8)]=>[4,5,6,3,1,2,8,7]=>[4,3,1] [(1,6),(2,5),(3,4),(7,8)]=>[4,5,6,3,2,1,8,7]=>[4,2,1,1] [(1,7),(2,5),(3,4),(6,8)]=>[4,5,7,3,2,8,1,6]=>[4,2,1,1] [(1,8),(2,5),(3,4),(6,7)]=>[4,5,7,3,2,8,6,1]=>[4,2,1,1] [(1,8),(2,6),(3,4),(5,7)]=>[4,6,7,3,8,2,5,1]=>[4,2,1,1] [(1,7),(2,6),(3,4),(5,8)]=>[4,6,7,3,8,2,1,5]=>[4,2,1,1] [(1,6),(2,7),(3,4),(5,8)]=>[4,6,7,3,8,1,2,5]=>[4,3,1] [(1,5),(2,7),(3,4),(6,8)]=>[4,5,7,3,1,8,2,6]=>[4,3,1] [(1,4),(2,7),(3,5),(6,8)]=>[4,5,7,1,3,8,2,6]=>[4,3,1] [(1,3),(2,7),(4,5),(6,8)]=>[3,5,1,7,4,8,2,6]=>[4,3,1] [(1,2),(3,7),(4,5),(6,8)]=>[2,1,5,7,4,8,3,6]=>[4,3,1] [(1,2),(3,8),(4,5),(6,7)]=>[2,1,5,7,4,8,6,3]=>[4,3,1] [(1,3),(2,8),(4,5),(6,7)]=>[3,5,1,7,4,8,6,2]=>[4,3,1] [(1,4),(2,8),(3,5),(6,7)]=>[4,5,7,1,3,8,6,2]=>[4,3,1] [(1,5),(2,8),(3,4),(6,7)]=>[4,5,7,3,1,8,6,2]=>[4,2,2] [(1,6),(2,8),(3,4),(5,7)]=>[4,6,7,3,8,1,5,2]=>[4,2,2] [(1,7),(2,8),(3,4),(5,6)]=>[4,6,7,3,8,5,1,2]=>[4,2,2] [(1,8),(2,7),(3,4),(5,6)]=>[4,6,7,3,8,5,2,1]=>[4,2,1,1] [(1,8),(2,7),(3,5),(4,6)]=>[5,6,7,8,3,4,2,1]=>[4,2,1,1] [(1,7),(2,8),(3,5),(4,6)]=>[5,6,7,8,3,4,1,2]=>[4,2,2] [(1,6),(2,8),(3,5),(4,7)]=>[5,6,7,8,3,1,4,2]=>[4,2,2] [(1,5),(2,8),(3,6),(4,7)]=>[5,6,7,8,1,3,4,2]=>[4,3,1] [(1,4),(2,8),(3,6),(5,7)]=>[4,6,7,1,8,3,5,2]=>[4,3,1] [(1,3),(2,8),(4,6),(5,7)]=>[3,6,1,7,8,4,5,2]=>[4,3,1] [(1,2),(3,8),(4,6),(5,7)]=>[2,1,6,7,8,4,5,3]=>[4,3,1] [(1,2),(3,7),(4,6),(5,8)]=>[2,1,6,7,8,4,3,5]=>[4,3,1] [(1,3),(2,7),(4,6),(5,8)]=>[3,6,1,7,8,4,2,5]=>[4,3,1] [(1,4),(2,7),(3,6),(5,8)]=>[4,6,7,1,8,3,2,5]=>[4,3,1] [(1,5),(2,7),(3,6),(4,8)]=>[5,6,7,8,1,3,2,4]=>[4,3,1] [(1,6),(2,7),(3,5),(4,8)]=>[5,6,7,8,3,1,2,4]=>[4,3,1] [(1,7),(2,6),(3,5),(4,8)]=>[5,6,7,8,3,2,1,4]=>[4,2,1,1] [(1,8),(2,6),(3,5),(4,7)]=>[5,6,7,8,3,2,4,1]=>[4,2,1,1] [(1,8),(2,5),(3,6),(4,7)]=>[5,6,7,8,2,3,4,1]=>[4,3,1] [(1,7),(2,5),(3,6),(4,8)]=>[5,6,7,8,2,3,1,4]=>[4,3,1] [(1,6),(2,5),(3,7),(4,8)]=>[5,6,7,8,2,1,3,4]=>[4,3,1] [(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[4,4] [(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[4,4] [(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[4,4] [(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[4,4] [(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[4,4] [(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[4,4] [(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[4,4] [(1,5),(2,4),(3,7),(6,8)]=>[4,5,7,2,1,8,3,6]=>[4,3,1] [(1,6),(2,4),(3,7),(5,8)]=>[4,6,7,2,8,1,3,5]=>[4,3,1] [(1,7),(2,4),(3,6),(5,8)]=>[4,6,7,2,8,3,1,5]=>[4,3,1] [(1,8),(2,4),(3,6),(5,7)]=>[4,6,7,2,8,3,5,1]=>[4,3,1] [(1,8),(2,3),(4,6),(5,7)]=>[3,6,2,7,8,4,5,1]=>[4,3,1] [(1,7),(2,3),(4,6),(5,8)]=>[3,6,2,7,8,4,1,5]=>[4,3,1] [(1,6),(2,3),(4,7),(5,8)]=>[3,6,2,7,8,1,4,5]=>[4,3,1] [(1,5),(2,3),(4,7),(6,8)]=>[3,5,2,7,1,8,4,6]=>[4,3,1] [(1,4),(2,3),(5,7),(6,8)]=>[3,4,2,1,7,8,5,6]=>[4,3,1] [(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[4,4] [(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[4,4] [(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,7,8,6,5]=>[4,3,1] [(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,7,8,6,5]=>[4,3,1] [(1,4),(2,3),(5,8),(6,7)]=>[3,4,2,1,7,8,6,5]=>[4,2,2] [(1,5),(2,3),(4,8),(6,7)]=>[3,5,2,7,1,8,6,4]=>[4,2,2] [(1,6),(2,3),(4,8),(5,7)]=>[3,6,2,7,8,1,5,4]=>[4,2,2] [(1,7),(2,3),(4,8),(5,6)]=>[3,6,2,7,8,5,1,4]=>[4,2,2] [(1,8),(2,3),(4,7),(5,6)]=>[3,6,2,7,8,5,4,1]=>[4,2,1,1] [(1,8),(2,4),(3,7),(5,6)]=>[4,6,7,2,8,5,3,1]=>[4,2,1,1] [(1,7),(2,4),(3,8),(5,6)]=>[4,6,7,2,8,5,1,3]=>[4,2,2] [(1,6),(2,4),(3,8),(5,7)]=>[4,6,7,2,8,1,5,3]=>[4,2,2] [(1,5),(2,4),(3,8),(6,7)]=>[4,5,7,2,1,8,6,3]=>[4,2,2] [(1,4),(2,5),(3,8),(6,7)]=>[4,5,7,1,2,8,6,3]=>[4,3,1] [(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,7,2,8,6,4]=>[4,3,1] [(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,7,3,8,6,4]=>[4,3,1] [(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,7,8,3,5,4]=>[4,3,1] [(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,7,8,2,5,4]=>[4,3,1] [(1,4),(2,6),(3,8),(5,7)]=>[4,6,7,1,8,2,5,3]=>[4,3,1] [(1,5),(2,6),(3,8),(4,7)]=>[5,6,7,8,1,2,4,3]=>[4,3,1] [(1,6),(2,5),(3,8),(4,7)]=>[5,6,7,8,2,1,4,3]=>[4,2,2] [(1,7),(2,5),(3,8),(4,6)]=>[5,6,7,8,2,4,1,3]=>[4,2,2] [(1,8),(2,5),(3,7),(4,6)]=>[5,6,7,8,2,4,3,1]=>[4,2,1,1] [(1,8),(2,6),(3,7),(4,5)]=>[5,6,7,8,4,2,3,1]=>[4,2,1,1] [(1,7),(2,6),(3,8),(4,5)]=>[5,6,7,8,4,2,1,3]=>[4,2,1,1] [(1,6),(2,7),(3,8),(4,5)]=>[5,6,7,8,4,1,2,3]=>[4,3,1] [(1,5),(2,7),(3,8),(4,6)]=>[5,6,7,8,1,4,2,3]=>[4,3,1] [(1,4),(2,7),(3,8),(5,6)]=>[4,6,7,1,8,5,2,3]=>[4,3,1] [(1,3),(2,7),(4,8),(5,6)]=>[3,6,1,7,8,5,2,4]=>[4,3,1] [(1,2),(3,7),(4,8),(5,6)]=>[2,1,6,7,8,5,3,4]=>[4,3,1] [(1,2),(3,8),(4,7),(5,6)]=>[2,1,6,7,8,5,4,3]=>[4,2,1,1] [(1,3),(2,8),(4,7),(5,6)]=>[3,6,1,7,8,5,4,2]=>[4,2,1,1] [(1,4),(2,8),(3,7),(5,6)]=>[4,6,7,1,8,5,3,2]=>[4,2,1,1] [(1,5),(2,8),(3,7),(4,6)]=>[5,6,7,8,1,4,3,2]=>[4,2,1,1] [(1,6),(2,8),(3,7),(4,5)]=>[5,6,7,8,4,1,3,2]=>[4,2,1,1] [(1,7),(2,8),(3,6),(4,5)]=>[5,6,7,8,4,3,1,2]=>[4,2,1,1] [(1,8),(2,7),(3,6),(4,5)]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1] [(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5] [(1,4),(2,3),(5,6),(7,8),(9,10)]=>[3,4,2,1,6,5,8,7,10,9]=>[5,4,1] [(1,6),(2,3),(4,5),(7,8),(9,10)]=>[3,5,2,6,4,1,8,7,10,9]=>[5,4,1] [(1,8),(2,3),(4,5),(6,7),(9,10)]=>[3,5,2,7,4,8,6,1,10,9]=>[5,4,1] [(1,10),(2,3),(4,5),(6,7),(8,9)]=>[3,5,2,7,4,9,6,10,8,1]=>[5,4,1] [(1,2),(3,6),(4,5),(7,8),(9,10)]=>[2,1,5,6,4,3,8,7,10,9]=>[5,4,1] [(1,6),(2,5),(3,4),(7,8),(9,10)]=>[4,5,6,3,2,1,8,7,10,9]=>[5,3,1,1] [(1,8),(2,5),(3,4),(6,7),(9,10)]=>[4,5,7,3,2,8,6,1,10,9]=>[5,3,1,1] [(1,10),(2,5),(3,4),(6,7),(8,9)]=>[4,5,7,3,2,9,6,10,8,1]=>[5,3,1,1] [(1,2),(3,8),(4,5),(6,7),(9,10)]=>[2,1,5,7,4,8,6,3,10,9]=>[5,4,1] [(1,8),(2,7),(3,4),(5,6),(9,10)]=>[4,6,7,3,8,5,2,1,10,9]=>[5,3,1,1] [(1,10),(2,7),(3,4),(5,6),(8,9)]=>[4,6,7,3,9,5,2,10,8,1]=>[5,3,1,1] [(1,2),(3,10),(4,5),(6,7),(8,9)]=>[2,1,5,7,4,9,6,10,8,3]=>[5,4,1] [(1,10),(2,9),(3,4),(5,6),(7,8)]=>[4,6,8,3,9,5,10,7,2,1]=>[5,3,1,1] [(1,2),(3,4),(5,8),(6,7),(9,10)]=>[2,1,4,3,7,8,6,5,10,9]=>[5,4,1] [(1,4),(2,3),(5,8),(6,7),(9,10)]=>[3,4,2,1,7,8,6,5,10,9]=>[5,3,2] [(1,8),(2,3),(4,7),(5,6),(9,10)]=>[3,6,2,7,8,5,4,1,10,9]=>[5,3,1,1] [(1,10),(2,3),(4,7),(5,6),(8,9)]=>[3,6,2,7,9,5,4,10,8,1]=>[5,3,1,1] [(1,2),(3,8),(4,7),(5,6),(9,10)]=>[2,1,6,7,8,5,4,3,10,9]=>[5,3,1,1] [(1,8),(2,7),(3,6),(4,5),(9,10)]=>[5,6,7,8,4,3,2,1,10,9]=>[5,2,1,1,1] [(1,10),(2,7),(3,6),(4,5),(8,9)]=>[5,6,7,9,4,3,2,10,8,1]=>[5,2,1,1,1] [(1,2),(3,10),(4,7),(5,6),(8,9)]=>[2,1,6,7,9,5,4,10,8,3]=>[5,3,1,1] [(1,10),(2,9),(3,6),(4,5),(7,8)]=>[5,6,8,9,4,3,10,7,2,1]=>[5,2,1,1,1] [(1,2),(3,4),(5,10),(6,7),(8,9)]=>[2,1,4,3,7,9,6,10,8,5]=>[5,4,1] [(1,4),(2,3),(5,10),(6,7),(8,9)]=>[3,4,2,1,7,9,6,10,8,5]=>[5,3,2] [(1,10),(2,3),(4,9),(5,6),(7,8)]=>[3,6,2,8,9,5,10,7,4,1]=>[5,3,1,1] [(1,2),(3,10),(4,9),(5,6),(7,8)]=>[2,1,6,8,9,5,10,7,4,3]=>[5,3,1,1] [(1,10),(2,9),(3,8),(4,5),(6,7)]=>[5,7,8,9,4,10,6,3,2,1]=>[5,2,1,1,1] [(1,2),(3,4),(5,6),(7,10),(8,9)]=>[2,1,4,3,6,5,9,10,8,7]=>[5,4,1] [(1,4),(2,3),(5,6),(7,10),(8,9)]=>[3,4,2,1,6,5,9,10,8,7]=>[5,3,2] [(1,6),(2,3),(4,5),(7,10),(8,9)]=>[3,5,2,6,4,1,9,10,8,7]=>[5,3,2] [(1,10),(2,3),(4,5),(6,9),(7,8)]=>[3,5,2,8,4,9,10,7,6,1]=>[5,3,1,1] [(1,2),(3,6),(4,5),(7,10),(8,9)]=>[2,1,5,6,4,3,9,10,8,7]=>[5,3,2] [(1,6),(2,5),(3,4),(7,10),(8,9)]=>[4,5,6,3,2,1,9,10,8,7]=>[5,2,2,1] [(1,10),(2,5),(3,4),(6,9),(7,8)]=>[4,5,8,3,2,9,10,7,6,1]=>[5,2,2,1] [(1,2),(3,10),(4,5),(6,9),(7,8)]=>[2,1,5,8,4,9,10,7,6,3]=>[5,3,1,1] [(1,10),(2,9),(3,4),(5,8),(6,7)]=>[4,7,8,3,9,10,6,5,2,1]=>[5,2,1,1,1] [(1,2),(3,4),(5,10),(6,9),(7,8)]=>[2,1,4,3,8,9,10,7,6,5]=>[5,3,1,1] [(1,4),(2,3),(5,10),(6,9),(7,8)]=>[3,4,2,1,8,9,10,7,6,5]=>[5,2,2,1] [(1,10),(2,3),(4,9),(5,8),(6,7)]=>[3,7,2,8,9,10,6,5,4,1]=>[5,2,1,1,1] [(1,2),(3,10),(4,9),(5,8),(6,7)]=>[2,1,7,8,9,10,6,5,4,3]=>[5,2,1,1,1] [(1,10),(2,9),(3,8),(4,7),(5,6)]=>[6,7,8,9,10,5,4,3,2,1]=>[5,1,1,1,1,1] [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>[6,1,1,1,1,1,1] [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[2,1,7,8,9,10,6,5,4,3,12,11]=>[6,3,1,1,1] [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>[3,7,2,8,9,11,6,5,4,12,10,1]=>[6,3,1,1,1] [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[2,1,7,8,9,11,6,5,4,12,10,3]=>[6,3,1,1,1] [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[3,7,2,8,9,10,6,5,4,1,12,11]=>[6,3,1,1,1] [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[4,7,8,3,10,11,6,5,12,9,2,1]=>[6,3,1,1,1] [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[2,1,4,3,7,8,6,5,10,9,12,11]=>[6,5,1] [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>[3,7,2,8,10,11,6,5,12,9,4,1]=>[6,3,1,1,1] [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[2,1,7,8,10,11,6,5,12,9,4,3]=>[6,3,1,1,1] [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[3,4,2,1,7,8,6,5,10,9,12,11]=>[6,4,2] [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[4,7,8,3,9,11,6,5,2,12,10,1]=>[6,3,1,1,1] [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[2,1,4,3,7,8,6,5,11,12,10,9]=>[6,4,2] [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>[4,7,8,3,9,10,6,5,2,1,12,11]=>[6,3,1,1,1] [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>[3,4,2,1,7,8,6,5,11,12,10,9]=>[6,3,3] [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[5,7,9,10,4,11,6,12,8,3,2,1]=>[6,3,1,1,1] [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[2,1,5,7,4,9,6,10,8,3,12,11]=>[6,5,1] [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>[6,5,1] [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[2,1,5,7,4,9,6,11,8,12,10,3]=>[6,5,1] [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[3,5,2,7,4,9,6,10,8,1,12,11]=>[6,5,1] [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[4,7,9,3,10,11,6,12,8,5,2,1]=>[6,3,1,1,1] [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[2,1,4,3,7,9,6,10,8,5,12,11]=>[6,5,1] [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>[3,7,2,9,10,11,6,12,8,5,4,1]=>[6,3,1,1,1] [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[2,1,7,9,10,11,6,12,8,5,4,3]=>[6,3,1,1,1] [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[3,4,2,1,7,9,6,10,8,5,12,11]=>[6,4,2] [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[4,5,7,3,2,9,6,11,8,12,10,1]=>[6,4,1,1] [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[2,1,4,3,7,9,6,11,8,12,10,5]=>[6,5,1] [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>[4,5,7,3,2,9,6,10,8,1,12,11]=>[6,4,1,1] [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>[3,4,2,1,7,9,6,11,8,12,10,5]=>[6,4,2] [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[5,7,8,10,4,11,6,3,12,9,2,1]=>[6,3,1,1,1] [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[2,1,5,7,4,8,6,3,10,9,12,11]=>[6,5,1] [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>[3,5,2,7,4,10,6,11,12,9,8,1]=>[6,4,1,1] [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[2,1,5,7,4,10,6,11,12,9,8,3]=>[6,4,1,1] [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[3,5,2,7,4,8,6,1,10,9,12,11]=>[6,5,1] [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[5,7,8,9,4,11,6,3,2,12,10,1]=>[6,3,1,1,1] [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[2,1,5,7,4,8,6,3,11,12,10,9]=>[6,4,2] [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[5,7,8,9,4,10,6,3,2,1,12,11]=>[6,3,1,1,1] [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>[3,5,2,7,4,8,6,1,11,12,10,9]=>[6,4,2] [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>[4,5,7,3,2,10,6,11,12,9,8,1]=>[6,3,2,1] [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[2,1,4,3,7,10,6,11,12,9,8,5]=>[6,4,1,1] [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[4,5,7,3,2,8,6,1,10,9,12,11]=>[6,4,1,1] [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>[3,4,2,1,7,10,6,11,12,9,8,5]=>[6,3,2,1] [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[4,5,7,3,2,8,6,1,11,12,10,9]=>[6,3,2,1] [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[6,8,9,10,11,5,12,7,4,3,2,1]=>[6,2,1,1,1,1] [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[2,1,6,8,9,5,10,7,4,3,12,11]=>[6,4,1,1] [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>[3,6,2,8,9,5,11,7,4,12,10,1]=>[6,4,1,1] [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[2,1,6,8,9,5,11,7,4,12,10,3]=>[6,4,1,1] [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[3,6,2,8,9,5,10,7,4,1,12,11]=>[6,4,1,1] [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[4,6,8,3,10,5,11,7,12,9,2,1]=>[6,4,1,1] [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6] [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>[3,6,2,8,10,5,11,7,12,9,4,1]=>[6,4,1,1] [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[2,1,6,8,10,5,11,7,12,9,4,3]=>[6,4,1,1] [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[3,4,2,1,6,5,8,7,10,9,12,11]=>[6,5,1] [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[4,6,8,3,9,5,11,7,2,12,10,1]=>[6,4,1,1] [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[2,1,4,3,6,5,8,7,11,12,10,9]=>[6,5,1] [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>[4,6,8,3,9,5,10,7,2,1,12,11]=>[6,4,1,1] [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>[3,4,2,1,6,5,8,7,11,12,10,9]=>[6,4,2] [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[5,8,9,10,4,11,12,7,6,3,2,1]=>[6,2,1,1,1,1] [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[2,1,5,8,4,9,10,7,6,3,12,11]=>[6,4,1,1] [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>[3,5,2,8,4,9,11,7,6,12,10,1]=>[6,4,1,1] [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[2,1,5,8,4,9,11,7,6,12,10,3]=>[6,4,1,1] [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[3,5,2,8,4,9,10,7,6,1,12,11]=>[6,4,1,1] [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[4,8,9,3,10,11,12,7,6,5,2,1]=>[6,2,1,1,1,1] [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[2,1,4,3,8,9,10,7,6,5,12,11]=>[6,4,1,1] [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>[3,8,2,9,10,11,12,7,6,5,4,1]=>[6,2,1,1,1,1] [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[2,1,8,9,10,11,12,7,6,5,4,3]=>[6,2,1,1,1,1] [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[3,4,2,1,8,9,10,7,6,5,12,11]=>[6,3,2,1] [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[4,5,8,3,2,9,11,7,6,12,10,1]=>[6,3,2,1] [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[2,1,4,3,8,9,11,7,6,12,10,5]=>[6,4,1,1] [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>[4,5,8,3,2,9,10,7,6,1,12,11]=>[6,3,2,1] [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>[3,4,2,1,8,9,11,7,6,12,10,5]=>[6,3,2,1] [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[5,6,8,10,4,3,11,7,12,9,2,1]=>[6,3,1,1,1] [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[2,1,5,6,4,3,8,7,10,9,12,11]=>[6,5,1] [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>[3,5,2,8,4,10,11,7,12,9,6,1]=>[6,4,1,1] [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[2,1,5,8,4,10,11,7,12,9,6,3]=>[6,4,1,1] [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[3,5,2,6,4,1,8,7,10,9,12,11]=>[6,5,1] [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[5,6,8,9,4,3,11,7,2,12,10,1]=>[6,3,1,1,1] [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[2,1,5,6,4,3,8,7,11,12,10,9]=>[6,4,2] [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[5,6,8,9,4,3,10,7,2,1,12,11]=>[6,3,1,1,1] [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>[3,5,2,6,4,1,8,7,11,12,10,9]=>[6,4,2] [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>[4,5,8,3,2,10,11,7,12,9,6,1]=>[6,3,2,1] [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[2,1,4,3,8,10,11,7,12,9,6,5]=>[6,4,1,1] [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[4,5,6,3,2,1,8,7,10,9,12,11]=>[6,4,1,1] [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>[3,4,2,1,8,10,11,7,12,9,6,5]=>[6,3,2,1] [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[4,5,6,3,2,1,8,7,11,12,10,9]=>[6,3,2,1] [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[6,7,9,10,11,5,4,12,8,3,2,1]=>[6,2,1,1,1,1] [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[2,1,6,7,9,5,4,10,8,3,12,11]=>[6,4,1,1] [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>[3,6,2,7,9,5,4,11,8,12,10,1]=>[6,4,1,1] [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[2,1,6,7,9,5,4,11,8,12,10,3]=>[6,4,1,1] [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[3,6,2,7,9,5,4,10,8,1,12,11]=>[6,4,1,1] [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[4,6,9,3,10,5,11,12,8,7,2,1]=>[6,3,1,1,1] [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[2,1,4,3,6,5,9,10,8,7,12,11]=>[6,5,1] [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>[3,6,2,9,10,5,11,12,8,7,4,1]=>[6,3,1,1,1] [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[2,1,6,9,10,5,11,12,8,7,4,3]=>[6,3,1,1,1] [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[3,4,2,1,6,5,9,10,8,7,12,11]=>[6,4,2] [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[4,6,7,3,9,5,2,11,8,12,10,1]=>[6,4,1,1] [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[2,1,4,3,6,5,9,11,8,12,10,7]=>[6,5,1] [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>[4,6,7,3,9,5,2,10,8,1,12,11]=>[6,4,1,1] [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>[3,4,2,1,6,5,9,11,8,12,10,7]=>[6,4,2] [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[6,7,8,10,11,5,4,3,12,9,2,1]=>[6,2,1,1,1,1] [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[2,1,6,7,8,5,4,3,10,9,12,11]=>[6,4,1,1] [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>[3,6,2,7,10,5,4,11,12,9,8,1]=>[6,3,2,1] [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[2,1,6,7,10,5,4,11,12,9,8,3]=>[6,3,2,1] [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[3,6,2,7,8,5,4,1,10,9,12,11]=>[6,4,1,1] [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>[6,7,8,9,11,5,4,3,2,12,10,1]=>[6,2,1,1,1,1] [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[2,1,6,7,8,5,4,3,11,12,10,9]=>[6,3,2,1] [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[6,7,8,9,10,5,4,3,2,1,12,11]=>[6,2,1,1,1,1] [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>[3,6,2,7,8,5,4,1,11,12,10,9]=>[6,3,2,1] [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>[4,6,7,3,10,5,2,11,12,9,8,1]=>[6,3,2,1] [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[2,1,4,3,6,5,10,11,12,9,8,7]=>[6,4,1,1] [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[4,6,7,3,8,5,2,1,10,9,12,11]=>[6,4,1,1] [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>[3,4,2,1,6,5,10,11,12,9,8,7]=>[6,3,2,1] [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[4,6,7,3,8,5,2,1,11,12,10,9]=>[6,3,2,1] [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[5,6,9,10,4,3,11,12,8,7,2,1]=>[6,2,2,1,1] [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[2,1,5,6,4,3,9,10,8,7,12,11]=>[6,4,2] [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>[3,5,2,9,4,10,11,12,8,7,6,1]=>[6,3,1,1,1] [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[2,1,5,9,4,10,11,12,8,7,6,3]=>[6,3,1,1,1] [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[3,5,2,6,4,1,9,10,8,7,12,11]=>[6,4,2] [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>[5,6,7,9,4,3,2,11,8,12,10,1]=>[6,3,1,1,1] [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[2,1,5,6,4,3,9,11,8,12,10,7]=>[6,4,2] [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[5,6,7,9,4,3,2,10,8,1,12,11]=>[6,3,1,1,1] [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>[3,5,2,6,4,1,9,11,8,12,10,7]=>[6,4,2] [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>[4,5,9,3,2,10,11,12,8,7,6,1]=>[6,2,2,1,1] [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[2,1,4,3,9,10,11,12,8,7,6,5]=>[6,3,1,1,1] [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[4,5,6,3,2,1,9,10,8,7,12,11]=>[6,3,2,1] [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>[3,4,2,1,9,10,11,12,8,7,6,5]=>[6,2,2,1,1] [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[4,5,6,3,2,1,9,11,8,12,10,7]=>[6,3,2,1] [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[5,6,7,10,4,3,2,11,12,9,8,1]=>[6,2,2,1,1] [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[2,1,5,6,4,3,10,11,12,9,8,7]=>[6,3,2,1] [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>[5,6,7,8,4,3,2,1,10,9,12,11]=>[6,3,1,1,1] [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>[3,5,2,6,4,1,10,11,12,9,8,7]=>[6,3,2,1] [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>[5,6,7,8,4,3,2,1,11,12,10,9]=>[6,2,2,1,1] [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>[4,5,6,3,2,1,10,11,12,9,8,7]=>[6,2,2,2]
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
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.