Identifier
Mp00201: Dyck paths RingelPermutations
Mp00066: Permutations inversePermutations
Mp00239: Permutations CorteelPermutations
Mp00069: Permutations complementPermutations
Mp00068: Permutations Simion-Schmidt mapPermutations
Images
=>
Cc0005;cc-rep-0
[1,0]=>[2,1]=>[2,1]=>[2,1]=>[1,2]=>[1,2] [1,0,1,0]=>[3,1,2]=>[2,3,1]=>[3,2,1]=>[1,2,3]=>[1,3,2] [1,1,0,0]=>[2,3,1]=>[3,1,2]=>[3,1,2]=>[1,3,2]=>[1,3,2] [1,0,1,0,1,0]=>[4,1,2,3]=>[2,3,4,1]=>[4,2,3,1]=>[1,3,2,4]=>[1,4,3,2] [1,0,1,1,0,0]=>[3,1,4,2]=>[2,4,1,3]=>[4,2,1,3]=>[1,3,4,2]=>[1,4,3,2] [1,1,0,0,1,0]=>[2,4,1,3]=>[3,1,4,2]=>[4,1,3,2]=>[1,4,2,3]=>[1,4,3,2] [1,1,0,1,0,0]=>[4,3,1,2]=>[3,4,2,1]=>[4,3,1,2]=>[1,2,4,3]=>[1,4,3,2] [1,1,1,0,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[4,1,2,3]=>[1,4,3,2]=>[1,4,3,2] [1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,5,4,3,2] [1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[2,3,5,1,4]=>[5,2,3,1,4]=>[1,4,3,5,2]=>[1,5,4,3,2] [1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[2,4,1,5,3]=>[5,2,1,4,3]=>[1,4,5,2,3]=>[1,5,4,3,2] [1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>[2,4,5,3,1]=>[5,2,4,1,3]=>[1,4,2,5,3]=>[1,5,4,3,2] [1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[1,5,4,3,2] [1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[3,1,4,5,2]=>[5,1,3,4,2]=>[1,5,3,2,4]=>[1,5,4,3,2] [1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[3,1,5,2,4]=>[5,1,3,2,4]=>[1,5,3,4,2]=>[1,5,4,3,2] [1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,4,2,5,1]=>[5,3,1,4,2]=>[1,3,5,2,4]=>[1,5,4,3,2] [1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>[3,4,5,2,1]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[1,5,4,3,2] [1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>[3,5,2,1,4]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[1,5,4,3,2] [1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[4,1,2,5,3]=>[5,1,2,4,3]=>[1,5,4,2,3]=>[1,5,4,3,2] [1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>[4,1,5,3,2]=>[5,1,4,2,3]=>[1,5,2,4,3]=>[1,5,4,3,2] [1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>[4,5,2,3,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[1,5,4,3,2] [1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[1,5,4,3,2] [1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>[1,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[2,3,5,1,6,4]=>[6,2,3,1,5,4]=>[1,5,4,6,2,3]=>[1,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>[1,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>[1,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[2,4,1,5,6,3]=>[6,2,1,4,5,3]=>[1,5,6,3,2,4]=>[1,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[2,4,1,6,3,5]=>[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>[1,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>[2,4,5,3,6,1]=>[6,2,4,1,5,3]=>[1,5,3,6,2,4]=>[1,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>[2,4,5,6,3,1]=>[6,2,5,4,1,3]=>[1,5,2,3,6,4]=>[1,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>[2,4,6,3,1,5]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>[1,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[2,5,1,3,6,4]=>[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>[1,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>[2,5,1,6,4,3]=>[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>[1,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>[2,5,6,3,4,1]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>[1,6,5,4,3,2] [1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[1,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[3,1,4,5,6,2]=>[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>[1,6,5,4,3,2] [1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[3,1,4,6,2,5]=>[6,1,3,4,2,5]=>[1,6,4,3,5,2]=>[1,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[3,1,5,2,6,4]=>[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>[1,6,5,4,3,2] [1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>[3,1,5,6,4,2]=>[6,1,3,5,2,4]=>[1,6,4,2,5,3]=>[1,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[3,1,6,2,4,5]=>[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>[1,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[6,3,1,4,5,2]=>[1,4,6,3,2,5]=>[1,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>[3,4,2,6,1,5]=>[6,3,1,4,2,5]=>[1,4,6,3,5,2]=>[1,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>[1,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>[3,4,5,6,1,2]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,6,5,4,3,2] [1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>[3,4,6,2,1,5]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[1,6,5,4,3,2] [1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>[3,5,2,1,6,4]=>[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>[1,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>[1,4,6,2,5,3]=>[1,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>[3,5,6,2,4,1]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[1,6,5,4,3,2] [1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>[3,6,2,1,4,5]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[1,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[4,1,2,5,6,3]=>[6,1,2,4,5,3]=>[1,6,5,3,2,4]=>[1,6,5,4,3,2] [1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[4,1,2,6,3,5]=>[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>[1,6,5,4,3,2] [1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>[4,1,5,3,6,2]=>[6,1,4,2,5,3]=>[1,6,3,5,2,4]=>[1,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>[4,1,5,6,3,2]=>[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>[1,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>[4,1,6,3,2,5]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>[1,6,5,4,3,2] [1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,5,2,3,6,1]=>[6,4,1,2,5,3]=>[1,3,6,5,2,4]=>[1,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>[4,5,2,6,3,1]=>[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>[1,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[1,6,5,4,3,2] [1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>[4,6,2,3,1,5]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[1,6,5,4,3,2] [1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[5,1,2,3,6,4]=>[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>[1,6,5,4,3,2] [1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>[5,1,2,6,4,3]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>[1,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>[5,1,6,3,4,2]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[1,6,5,4,3,2] [1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>[5,6,2,3,4,1]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[1,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[2,3,4,6,1,7,5]=>[7,2,3,4,1,6,5]=>[1,6,5,4,7,2,3]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>[1,6,5,4,2,7,3]=>[1,7,6,5,4,3,2] [1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[2,3,5,1,6,7,4]=>[7,2,3,1,5,6,4]=>[1,6,5,7,3,2,4]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[2,3,5,1,7,4,6]=>[7,2,3,1,5,4,6]=>[1,6,5,7,3,4,2]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,6,4]=>[1,6,5,3,7,2,4]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>[2,3,5,6,7,4,1]=>[7,2,3,6,5,1,4]=>[1,6,5,2,3,7,4]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>[2,3,5,7,4,1,6]=>[7,2,3,5,1,4,6]=>[1,6,5,3,7,4,2]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[2,3,6,1,4,7,5]=>[7,2,3,1,4,6,5]=>[1,6,5,7,4,2,3]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>[2,3,6,1,7,5,4]=>[7,2,3,1,6,4,5]=>[1,6,5,7,2,4,3]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>[2,3,6,7,4,5,1]=>[7,2,3,6,1,4,5]=>[1,6,5,2,7,4,3]=>[1,7,6,5,4,3,2] [1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[2,4,1,5,6,7,3]=>[7,2,1,4,5,6,3]=>[1,6,7,4,3,2,5]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[2,4,1,5,7,3,6]=>[7,2,1,4,5,3,6]=>[1,6,7,4,3,5,2]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[2,4,1,6,3,7,5]=>[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>[2,4,1,6,7,5,3]=>[7,2,1,4,6,3,5]=>[1,6,7,4,2,5,3]=>[1,7,6,5,4,3,2] [1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[2,4,1,7,3,5,6]=>[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>[2,4,5,3,6,7,1]=>[7,2,4,1,5,6,3]=>[1,6,4,7,3,2,5]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>[2,4,5,3,7,1,6]=>[7,2,4,1,5,3,6]=>[1,6,4,7,3,5,2]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>[2,4,5,6,3,7,1]=>[7,2,5,4,1,6,3]=>[1,6,3,4,7,2,5]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>[2,4,5,6,7,1,3]=>[7,2,6,4,5,3,1]=>[1,6,2,4,3,5,7]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>[2,4,5,7,3,1,6]=>[7,2,5,4,1,3,6]=>[1,6,3,4,7,5,2]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>[2,4,6,3,1,7,5]=>[7,2,4,1,3,6,5]=>[1,6,4,7,5,2,3]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>[2,4,6,3,7,5,1]=>[7,2,4,1,6,3,5]=>[1,6,4,7,2,5,3]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>[2,4,6,7,3,5,1]=>[7,2,6,4,1,3,5]=>[1,6,2,4,7,5,3]=>[1,7,6,5,4,3,2] [1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>[2,4,7,3,1,5,6]=>[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[2,5,1,3,6,7,4]=>[7,2,1,3,5,6,4]=>[1,6,7,5,3,2,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[2,5,1,3,7,4,6]=>[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>[2,5,1,6,4,7,3]=>[7,2,1,5,3,6,4]=>[1,6,7,3,5,2,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>[2,5,1,6,7,4,3]=>[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>[2,5,1,7,4,3,6]=>[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>[2,5,6,3,4,7,1]=>[7,2,5,1,3,6,4]=>[1,6,3,7,5,2,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>[2,5,6,3,7,4,1]=>[7,2,6,1,5,3,4]=>[1,6,2,7,3,5,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>[2,5,6,7,4,3,1]=>[7,2,6,5,1,3,4]=>[1,6,2,3,7,5,4]=>[1,7,6,5,4,3,2] [1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>[2,5,7,3,4,1,6]=>[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[2,6,1,3,4,7,5]=>[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>[2,6,1,3,7,5,4]=>[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>[2,6,1,7,4,5,3]=>[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>[2,6,7,3,4,5,1]=>[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>[1,7,6,5,4,3,2] [1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[3,1,4,5,7,2,6]=>[7,1,3,4,5,2,6]=>[1,7,5,4,3,6,2]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[3,1,4,6,2,7,5]=>[7,1,3,4,2,6,5]=>[1,7,5,4,6,2,3]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>[3,1,4,6,7,5,2]=>[7,1,3,4,6,2,5]=>[1,7,5,4,2,6,3]=>[1,7,6,5,4,3,2] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[3,1,4,7,2,5,6]=>[7,1,3,4,2,5,6]=>[1,7,5,4,6,3,2]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[3,1,5,2,6,7,4]=>[7,1,3,2,5,6,4]=>[1,7,5,6,3,2,4]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[3,1,5,2,7,4,6]=>[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>[3,1,5,6,4,7,2]=>[7,1,3,5,2,6,4]=>[1,7,5,3,6,2,4]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>[3,1,5,6,7,4,2]=>[7,1,3,6,5,2,4]=>[1,7,5,2,3,6,4]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>[3,1,5,7,4,2,6]=>[7,1,3,5,2,4,6]=>[1,7,5,3,6,4,2]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[3,1,6,2,4,7,5]=>[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>[3,1,6,2,7,5,4]=>[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>[3,1,6,7,4,5,2]=>[7,1,3,6,2,4,5]=>[1,7,5,2,6,4,3]=>[1,7,6,5,4,3,2] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[3,1,7,2,4,5,6]=>[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[7,3,1,4,5,6,2]=>[1,5,7,4,3,2,6]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>[3,4,2,5,7,1,6]=>[7,3,1,4,5,2,6]=>[1,5,7,4,3,6,2]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>[3,4,2,6,1,7,5]=>[7,3,1,4,2,6,5]=>[1,5,7,4,6,2,3]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>[3,4,2,6,7,5,1]=>[7,3,1,4,6,2,5]=>[1,5,7,4,2,6,3]=>[1,7,6,5,4,3,2] [1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>[3,4,2,7,1,5,6]=>[7,3,1,4,2,5,6]=>[1,5,7,4,6,3,2]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[7,4,3,1,5,6,2]=>[1,4,5,7,3,2,6]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>[3,4,5,2,7,1,6]=>[7,4,3,1,5,2,6]=>[1,4,5,7,3,6,2]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>[3,4,5,6,1,7,2]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>[3,4,5,7,1,2,6]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>[3,4,6,2,1,7,5]=>[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>[3,4,6,2,7,5,1]=>[7,4,3,1,6,2,5]=>[1,4,5,7,2,6,3]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>[3,4,6,7,1,5,2]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>[1,7,6,5,4,3,2] [1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>[3,4,7,2,1,5,6]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>[3,5,2,1,6,7,4]=>[7,3,1,2,5,6,4]=>[1,5,7,6,3,2,4]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>[3,5,2,1,7,4,6]=>[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>[3,5,2,6,4,7,1]=>[7,3,1,5,2,6,4]=>[1,5,7,3,6,2,4]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>[3,5,2,6,7,4,1]=>[7,3,1,6,5,2,4]=>[1,5,7,2,3,6,4]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>[3,5,2,7,4,1,6]=>[7,3,1,5,2,4,6]=>[1,5,7,3,6,4,2]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>[3,5,6,2,4,7,1]=>[7,5,3,1,2,6,4]=>[1,3,5,7,6,2,4]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>[3,5,6,2,7,4,1]=>[7,6,3,1,5,2,4]=>[1,2,5,7,3,6,4]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>[3,5,6,7,4,1,2]=>[7,6,3,5,1,4,2]=>[1,2,5,3,7,4,6]=>[1,7,6,5,4,3,2] [1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>[3,5,7,2,4,1,6]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>[3,6,2,1,4,7,5]=>[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>[3,6,2,1,7,5,4]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>[3,6,2,7,4,5,1]=>[7,3,1,6,2,4,5]=>[1,5,7,2,6,4,3]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>[3,6,7,2,4,5,1]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[1,7,6,5,4,3,2] [1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>[3,7,2,1,4,5,6]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[4,1,2,5,6,7,3]=>[7,1,2,4,5,6,3]=>[1,7,6,4,3,2,5]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[4,1,2,5,7,3,6]=>[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[4,1,2,6,3,7,5]=>[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>[4,1,2,6,7,5,3]=>[7,1,2,4,6,3,5]=>[1,7,6,4,2,5,3]=>[1,7,6,5,4,3,2] [1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[4,1,2,7,3,5,6]=>[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>[4,1,5,3,6,7,2]=>[7,1,4,2,5,6,3]=>[1,7,4,6,3,2,5]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>[4,1,5,3,7,2,6]=>[7,1,4,2,5,3,6]=>[1,7,4,6,3,5,2]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>[4,1,5,6,3,7,2]=>[7,1,5,4,2,6,3]=>[1,7,3,4,6,2,5]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>[4,1,5,6,7,2,3]=>[7,1,6,4,5,3,2]=>[1,7,2,4,3,5,6]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>[4,1,5,7,3,2,6]=>[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>[4,1,6,3,2,7,5]=>[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>[4,1,6,3,7,5,2]=>[7,1,4,2,6,3,5]=>[1,7,4,6,2,5,3]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>[4,1,6,7,3,5,2]=>[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>[1,7,6,5,4,3,2] [1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>[4,1,7,3,2,5,6]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>[4,5,2,3,6,7,1]=>[7,4,1,2,5,6,3]=>[1,4,7,6,3,2,5]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>[4,5,2,3,7,1,6]=>[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>[4,5,2,6,3,7,1]=>[7,5,1,4,2,6,3]=>[1,3,7,4,6,2,5]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>[4,5,2,6,7,1,3]=>[7,6,1,4,5,3,2]=>[1,2,7,4,3,5,6]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>[4,5,2,7,3,1,6]=>[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,6,3]=>[1,3,4,7,6,2,5]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>[4,5,6,3,7,1,2]=>[7,6,4,1,5,3,2]=>[1,2,4,7,3,5,6]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>[4,5,6,7,3,1,2]=>[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>[1,7,6,5,4,3,2] [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>[4,5,7,3,2,1,6]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>[4,6,2,3,1,7,5]=>[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>[4,6,2,3,7,5,1]=>[7,4,1,2,6,3,5]=>[1,4,7,6,2,5,3]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>[4,6,2,7,3,5,1]=>[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>[4,6,7,3,2,5,1]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[1,7,6,5,4,3,2] [1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>[4,7,2,3,1,5,6]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[5,1,2,3,6,7,4]=>[7,1,2,3,5,6,4]=>[1,7,6,5,3,2,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[5,1,2,3,7,4,6]=>[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>[5,1,2,6,4,7,3]=>[7,1,2,5,3,6,4]=>[1,7,6,3,5,2,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>[5,1,2,6,7,4,3]=>[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>[5,1,2,7,4,3,6]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>[5,1,6,3,4,7,2]=>[7,1,5,2,3,6,4]=>[1,7,3,6,5,2,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>[5,1,6,3,7,4,2]=>[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>[5,1,6,7,4,3,2]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>[5,1,7,3,4,2,6]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[5,6,2,3,4,7,1]=>[7,5,1,2,3,6,4]=>[1,3,7,6,5,2,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>[5,6,2,3,7,4,1]=>[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>[5,6,2,7,4,3,1]=>[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>[5,6,7,3,4,2,1]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[1,7,6,5,4,3,2] [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>[5,7,2,3,4,1,6]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[6,1,2,3,4,7,5]=>[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>[6,1,2,3,7,5,4]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>[6,1,2,7,4,5,3]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>[6,1,7,3,4,5,2]=>[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>[1,7,6,5,4,3,2] [1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>[6,7,2,3,4,5,1]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[1,7,6,5,4,3,2] [1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
inverse
Description
Sends a permutation to its inverse.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
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].