Identifier
Mp00201:
Dyck paths
—Ringel⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00069: Permutations —complement⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[2,1]=>[1,2]=>[1,2]=>1
[1,0,1,0]=>[3,1,2]=>[1,3,2]=>[3,1,2]=>00
[1,1,0,0]=>[2,3,1]=>[2,1,3]=>[2,3,1]=>00
[1,0,1,0,1,0]=>[4,1,2,3]=>[1,4,3,2]=>[4,3,1,2]=>000
[1,0,1,1,0,0]=>[3,1,4,2]=>[2,4,1,3]=>[2,4,1,3]=>000
[1,1,0,0,1,0]=>[2,4,1,3]=>[3,1,4,2]=>[3,1,4,2]=>000
[1,1,0,1,0,0]=>[4,3,1,2]=>[1,2,4,3]=>[4,1,2,3]=>000
[1,1,1,0,0,0]=>[2,3,4,1]=>[3,2,1,4]=>[3,4,2,1]=>000
[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[5,4,3,1,2]=>0000
[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[2,5,4,1,3]=>[2,5,4,1,3]=>0000
[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[3,5,1,4,2]=>[5,3,4,1,2]=>0000
[1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>[1,5,2,4,3]=>[5,1,4,2,3]=>0000
[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[3,5,2,1,4]=>[3,5,2,1,4]=>0000
[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[4,3,1,5,2]=>0000
[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[4,5,2,3,1]=>0000
[1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[5,3,1,2,4]=>0000
[1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[5,4,1,2,3]=>0000
[1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>[2,3,5,1,4]=>[2,5,1,3,4]=>0000
[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[4,3,1,5,2]=>[4,1,5,3,2]=>0000
[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>[4,1,2,5,3]=>[4,1,2,5,3]=>0000
[1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>[1,3,2,5,4]=>[3,1,5,2,4]=>0000
[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[4,5,3,2,1]=>0000
[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000
[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[2,6,5,4,1,3]=>[2,6,5,4,1,3]=>00000
[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>[6,3,5,4,1,2]=>00000
[1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>[6,1,5,4,2,3]=>00000
[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>[3,6,5,2,1,4]=>00000
[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[6,4,3,5,1,2]=>00000
[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[4,6,2,5,1,3]=>00000
[1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>[6,5,1,3,2,4]=>00000
[1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[6,5,1,4,2,3]=>00000
[1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>[2,6,3,5,1,4]=>[2,6,1,5,3,4]=>00000
[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>[4,3,6,5,1,2]=>00000
[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>[4,6,1,2,5,3]=>[6,1,4,5,2,3]=>00000
[1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>[1,6,3,2,5,4]=>[3,1,6,5,2,4]=>00000
[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[4,6,3,2,1,5]=>[4,6,3,2,1,5]=>00000
[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[5,4,3,1,6,2]=>00000
[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>[5,6,2,1,4,3]=>00000
[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[5,3,6,1,4,2]=>00000
[1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>[5,1,6,2,4,3]=>[5,1,4,2,6,3]=>00000
[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>[5,6,3,2,4,1]=>00000
[1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[6,4,3,1,2,5]=>00000
[1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>[2,4,6,5,1,3]=>[2,6,4,1,3,5]=>00000
[1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[6,5,3,1,2,4]=>00000
[1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>[6,5,2,1,4,3]=>00000
[1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>[2,3,6,5,1,4]=>[2,6,5,1,3,4]=>00000
[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>[3,4,6,1,5,2]=>[6,3,4,1,2,5]=>00000
[1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>[1,4,6,2,5,3]=>[6,4,5,1,2,3]=>00000
[1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>[1,3,6,2,5,4]=>[6,3,5,1,2,4]=>00000
[1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>[3,4,6,2,1,5]=>[3,6,2,1,4,5]=>00000
[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[5,4,1,6,3,2]=>00000
[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[5,6,2,4,3,1]=>00000
[1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>[5,1,3,6,4,2]=>[5,3,1,2,6,4]=>00000
[1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>[5,1,2,6,4,3]=>[5,4,1,2,6,3]=>00000
[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>[5,2,3,6,1,4]=>[5,6,2,3,4,1]=>00000
[1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>[4,3,1,6,2,5]=>00000
[1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>[1,4,2,6,5,3]=>[6,4,1,5,2,3]=>00000
[1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>00000
[1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>[2,4,3,6,1,5]=>[4,6,2,3,1,5]=>00000
[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[5,1,6,4,3,2]=>00000
[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>[5,4,1,2,6,3]=>[5,1,2,6,4,3]=>00000
[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>[5,1,3,2,6,4]=>[5,1,6,3,4,2]=>00000
[1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>[4,1,6,3,2,5]=>00000
[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[5,6,4,3,2,1]=>00000
[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[2,7,6,5,4,1,3]=>[2,7,6,5,4,1,3]=>000000
[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[3,7,6,5,1,4,2]=>[7,3,6,5,4,1,2]=>000000
[1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>[7,1,6,5,4,2,3]=>000000
[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[3,7,6,5,2,1,4]=>[3,7,6,5,2,1,4]=>000000
[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[4,7,6,1,5,3,2]=>[7,6,4,5,3,1,2]=>000000
[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[4,7,6,2,5,1,3]=>[4,7,2,6,5,1,3]=>000000
[1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[7,6,1,5,3,2,4]=>000000
[1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>[7,6,1,5,4,2,3]=>000000
[1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>[2,7,6,3,5,1,4]=>[2,7,1,6,5,3,4]=>000000
[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[4,7,6,3,1,5,2]=>[4,3,7,6,5,1,2]=>000000
[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>[4,7,6,1,2,5,3]=>[7,1,4,6,5,2,3]=>000000
[1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>[1,7,6,3,2,5,4]=>[3,1,7,6,5,2,4]=>000000
[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[4,7,6,3,2,1,5]=>[4,7,6,3,2,1,5]=>000000
[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[5,7,1,6,4,3,2]=>[7,5,4,3,6,1,2]=>000000
[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[5,7,2,6,4,1,3]=>[5,7,6,2,4,1,3]=>000000
[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[5,7,3,6,1,4,2]=>[7,5,6,3,4,1,2]=>000000
[1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>[5,7,1,6,2,4,3]=>[7,1,5,4,6,2,3]=>000000
[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[5,7,3,6,2,1,4]=>[5,7,3,2,6,1,4]=>000000
[1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>[7,6,4,1,3,2,5]=>000000
[1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>[2,7,4,6,5,1,3]=>[2,7,6,1,4,3,5]=>000000
[1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>[7,6,5,1,3,2,4]=>000000
[1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>[2,7,1,6,5,4,3]=>[7,6,5,2,4,1,3]=>000000
[1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>[2,7,3,6,5,1,4]=>[2,7,6,1,5,3,4]=>000000
[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>[3,7,4,6,1,5,2]=>[7,3,6,1,4,2,5]=>000000
[1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>[1,7,4,6,2,5,3]=>[7,4,6,1,5,2,3]=>000000
[1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>[1,7,3,6,2,5,4]=>[7,3,6,1,5,2,4]=>000000
[1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>[3,7,4,6,2,1,5]=>[3,7,6,2,4,1,5]=>000000
[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[5,7,4,1,6,3,2]=>[5,4,3,7,6,1,2]=>000000
[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[5,7,4,2,6,1,3]=>[5,7,4,6,2,1,3]=>000000
[1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>[5,7,1,3,6,4,2]=>[7,5,1,3,6,2,4]=>000000
[1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>[5,7,1,2,6,4,3]=>[7,5,1,4,6,2,3]=>000000
[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>[5,7,2,3,6,1,4]=>[5,7,2,3,6,1,4]=>000000
[1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>[1,7,4,3,6,5,2]=>[7,4,1,6,3,2,5]=>000000
[1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>[7,4,1,6,5,2,3]=>000000
[1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>[7,6,1,2,5,3,4]=>000000
[1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>[2,7,4,3,6,1,5]=>[4,7,2,6,3,1,5]=>000000
[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[5,7,4,3,1,6,2]=>[5,4,7,6,3,1,2]=>000000
[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>[5,7,4,1,2,6,3]=>[5,1,4,7,6,2,3]=>000000
[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>[5,1,7,3,6,2,4]=>000000
[1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>[1,7,4,3,2,6,5]=>[4,1,7,6,3,2,5]=>000000
[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[5,7,4,3,2,1,6]=>[5,7,4,3,2,1,6]=>000000
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>[6,5,4,3,1,7,2]=>000000
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[6,2,7,5,4,1,3]=>[6,7,5,2,1,4,3]=>000000
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[6,3,7,5,1,4,2]=>[6,5,7,3,1,4,2]=>000000
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>[6,1,7,5,2,4,3]=>[6,1,5,4,2,7,3]=>000000
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[6,3,7,5,2,1,4]=>[6,7,3,2,1,5,4]=>000000
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[6,4,7,1,5,3,2]=>[6,4,3,7,1,5,2]=>000000
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[6,4,7,2,5,1,3]=>[6,7,4,5,2,3,1]=>000000
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>[6,1,7,3,5,4,2]=>[6,5,1,3,2,7,4]=>000000
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>[6,1,7,2,5,4,3]=>[6,5,1,4,2,7,3]=>000000
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>[6,2,7,3,5,1,4]=>[6,7,2,3,1,5,4]=>000000
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[6,4,7,3,1,5,2]=>[6,4,7,5,1,3,2]=>000000
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>[6,4,7,1,2,5,3]=>[6,1,4,7,2,5,3]=>000000
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>[6,1,7,3,2,5,4]=>[6,1,7,3,2,5,4]=>000000
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[6,4,7,3,2,1,5]=>[6,7,4,3,2,5,1]=>000000
[1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[7,5,4,3,1,2,6]=>000000
[1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>[2,5,7,6,4,1,3]=>[2,7,5,4,1,3,6]=>000000
[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>[3,5,7,6,1,4,2]=>[7,3,5,4,1,2,6]=>000000
[1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>[7,5,6,4,1,2,3]=>000000
[1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>[3,5,7,6,2,1,4]=>[3,7,5,2,1,4,6]=>000000
[1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[7,6,4,3,1,2,5]=>000000
[1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>[2,4,7,6,5,1,3]=>[2,7,6,4,1,3,5]=>000000
[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>000000
[1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000
[1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>[3,2,7,6,5,1,4]=>[3,7,6,2,1,5,4]=>000000
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>[3,4,7,6,1,5,2]=>[7,3,6,4,1,2,5]=>000000
[1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>[1,4,7,6,2,5,3]=>[7,4,6,5,1,2,3]=>000000
[1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>[3,1,7,6,2,5,4]=>[7,1,6,3,2,5,4]=>000000
[1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>[3,4,7,6,2,1,5]=>[3,7,6,2,1,4,5]=>000000
[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>[4,5,7,1,6,3,2]=>[7,4,3,5,1,2,6]=>000000
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>[4,5,7,2,6,1,3]=>[4,7,2,5,1,3,6]=>000000
[1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>[1,5,7,3,6,4,2]=>[7,5,3,6,1,2,4]=>000000
[1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>[1,5,7,2,6,4,3]=>[7,5,4,6,1,2,3]=>000000
[1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>[2,5,7,3,6,1,4]=>[5,7,2,6,1,3,4]=>000000
[1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>[1,4,7,3,6,5,2]=>[7,4,3,6,1,2,5]=>000000
[1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>[7,6,4,5,1,2,3]=>000000
[1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>[2,1,7,3,6,5,4]=>[7,6,2,3,1,5,4]=>000000
[1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>[2,4,7,3,6,1,5]=>[4,7,2,6,1,3,5]=>000000
[1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>[4,5,7,3,1,6,2]=>[4,3,7,5,1,2,6]=>000000
[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>[4,5,7,1,2,6,3]=>[7,4,5,6,1,2,3]=>000000
[1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>[1,5,7,3,2,6,4]=>[5,3,7,6,1,2,4]=>000000
[1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>[1,4,7,3,2,6,5]=>[4,3,7,6,1,2,5]=>000000
[1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>[4,5,7,3,2,1,6]=>[4,7,3,2,1,5,6]=>000000
[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]=>[6,5,4,1,7,3,2]=>000000
[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[6,5,2,7,4,1,3]=>[6,7,2,1,5,4,3]=>000000
[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[6,5,3,7,1,4,2]=>[6,3,7,1,5,4,2]=>000000
[1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>[6,5,1,7,2,4,3]=>[6,1,5,2,7,4,3]=>000000
[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[6,5,3,7,2,1,4]=>[6,7,5,3,4,2,1]=>000000
[1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>[6,1,4,7,5,3,2]=>[6,4,3,1,2,7,5]=>000000
[1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>[6,2,4,7,5,1,3]=>[6,7,2,1,4,5,3]=>000000
[1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>[6,1,3,7,5,4,2]=>[6,5,3,1,2,7,4]=>000000
[1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>[6,5,2,1,7,4,3]=>000000
[1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>[6,2,3,7,5,1,4]=>[6,7,2,1,3,5,4]=>000000
[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>[6,3,4,7,1,5,2]=>[6,3,7,1,4,5,2]=>000000
[1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>[6,1,4,7,2,5,3]=>[6,4,7,1,2,5,3]=>000000
[1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>[6,1,3,7,2,5,4]=>[6,3,7,1,2,5,4]=>000000
[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>[6,3,4,7,2,1,5]=>[6,7,3,2,4,5,1]=>000000
[1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>[5,4,3,1,7,2,6]=>000000
[1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>[2,5,4,7,6,1,3]=>[5,7,2,1,4,3,6]=>000000
[1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>[1,5,3,7,6,4,2]=>[7,5,3,1,6,2,4]=>000000
[1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>[2,5,1,7,6,4,3]=>[7,5,2,1,4,3,6]=>000000
[1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>[2,5,3,7,6,1,4]=>[5,7,2,1,6,3,4]=>000000
[1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[7,6,3,1,2,4,5]=>000000
[1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>[7,6,2,1,4,5,3]=>000000
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>[7,6,2,1,3,5,4]=>000000
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>[2,3,4,7,6,1,5]=>[2,7,6,1,3,4,5]=>000000
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>[3,5,4,7,1,6,2]=>[5,3,7,1,4,2,6]=>000000
[1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>[1,5,4,7,2,6,3]=>[5,4,7,1,6,2,3]=>000000
[1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>[1,5,3,7,2,6,4]=>[5,3,7,1,6,2,4]=>000000
[1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>[1,3,4,7,2,6,5]=>[7,3,6,1,2,4,5]=>000000
[1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>[3,5,4,7,2,1,6]=>[5,7,3,2,4,1,6]=>000000
[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]=>[6,5,1,7,4,3,2]=>000000
[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[6,5,4,2,7,1,3]=>[6,7,2,5,4,3,1]=>000000
[1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>[6,5,1,3,7,4,2]=>[6,5,1,3,7,4,2]=>000000
[1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>[6,5,1,2,7,4,3]=>[6,5,1,2,7,4,3]=>000000
[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>[6,5,2,3,7,1,4]=>[6,7,2,3,5,4,1]=>000000
[1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>[6,1,4,3,7,5,2]=>[6,4,1,7,3,5,2]=>000000
[1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>[6,1,4,2,7,5,3]=>[6,4,1,7,2,5,3]=>000000
[1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>[6,1,2,3,7,5,4]=>[6,5,1,2,3,7,4]=>000000
[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>[6,2,4,3,7,1,5]=>[6,7,2,4,3,5,1]=>000000
[1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>[5,4,1,7,3,2,6]=>000000
[1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>[1,5,4,2,7,6,3]=>[5,4,1,7,6,2,3]=>000000
[1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]=>[7,5,1,2,6,3,4]=>000000
[1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>[7,4,1,6,2,3,5]=>000000
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>[2,5,4,3,7,1,6]=>[5,7,2,4,3,1,6]=>000000
[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]=>[6,1,7,5,4,3,2]=>000000
[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>[6,5,4,1,2,7,3]=>[6,1,2,7,5,4,3]=>000000
[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>[6,5,1,3,2,7,4]=>[6,1,7,3,5,4,2]=>000000
[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>[6,1,4,3,2,7,5]=>[6,1,7,4,3,5,2]=>000000
[1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>[5,1,7,4,3,2,6]=>000000
[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[6,7,5,4,3,2,1]=>000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,1,2,3,4,5,8,6]=>[2,8,7,6,5,4,1,3]=>[2,8,7,6,5,4,1,3]=>0000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,1,2,3,4,7,5,6]=>[1,8,7,6,5,2,4,3]=>[8,1,7,6,5,4,2,3]=>0000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[3,8,7,6,5,2,1,4]=>[3,8,7,6,5,2,1,4]=>0000000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[4,8,7,6,3,1,5,2]=>[4,3,8,7,6,5,1,2]=>0000000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,1,2,3,6,7,4,5]=>[1,8,7,6,3,2,5,4]=>[3,1,8,7,6,5,2,4]=>0000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]=>[4,8,7,6,3,2,1,5]=>0000000
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[5,8,7,2,6,4,1,3]=>[5,8,7,2,6,4,1,3]=>0000000
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,1,2,5,3,4,6,7]=>[1,8,7,4,6,5,3,2]=>[8,7,6,1,4,3,2,5]=>0000000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,1,2,6,3,7,4,5]=>[1,8,7,3,6,2,5,4]=>[8,3,7,1,6,5,2,4]=>0000000
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[5,8,7,4,2,6,1,3]=>[5,8,4,7,6,2,1,3]=>0000000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[5,8,7,4,3,2,1,6]=>[5,8,7,4,3,2,1,6]=>0000000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,7,2,4,5,8,6]=>[6,8,2,7,5,4,1,3]=>[6,8,7,5,2,4,1,3]=>0000000
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[6,8,3,7,5,2,1,4]=>[6,8,7,3,2,5,1,4]=>0000000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[6,8,4,7,1,5,3,2]=>[8,6,4,7,3,5,1,2]=>0000000
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[6,8,4,7,2,5,1,3]=>[6,8,4,7,2,5,1,3]=>0000000
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,8,2,6,4,5,7]=>[6,8,1,7,3,5,4,2]=>[8,6,1,5,3,7,2,4]=>0000000
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>[6,8,2,7,3,5,1,4]=>[6,8,2,7,3,5,1,4]=>0000000
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[6,8,4,7,3,2,1,5]=>[6,8,4,3,2,7,1,5]=>0000000
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>[3,8,5,7,6,1,4,2]=>[8,3,7,5,1,4,2,6]=>0000000
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,5,2,3,4,6,7]=>[1,8,4,7,6,5,3,2]=>[8,7,6,4,1,3,2,5]=>0000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,1,7,2,3,4,5,6]=>[1,8,2,7,6,5,4,3]=>[8,7,6,5,1,4,2,3]=>0000000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,1,7,2,3,4,8,5]=>[3,8,2,7,6,5,1,4]=>[3,8,7,6,2,5,1,4]=>0000000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[8,1,5,2,3,7,4,6]=>[1,8,4,7,6,2,5,3]=>[8,4,7,6,1,5,2,3]=>0000000
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>[4,8,5,7,2,6,1,3]=>[4,8,2,7,1,5,3,6]=>0000000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>[2,8,5,7,3,6,1,4]=>[5,8,2,7,1,6,3,4]=>0000000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>[1,8,4,7,2,6,5,3]=>[8,7,4,6,1,5,2,3]=>0000000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]=>[2,8,4,7,3,6,1,5]=>[4,8,2,7,1,6,3,5]=>0000000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>[6,8,5,1,7,4,3,2]=>[6,5,4,3,8,7,1,2]=>0000000
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,4,7,2,5,8,6]=>[6,8,5,2,7,4,1,3]=>[6,8,5,2,7,4,1,3]=>0000000
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>[6,8,5,3,7,2,1,4]=>[6,8,5,3,7,2,1,4]=>0000000
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[8,1,6,5,2,7,3,4]=>[1,8,3,4,7,2,6,5]=>[8,3,7,1,2,6,4,5]=>0000000
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>[6,8,5,4,2,7,1,3]=>[6,8,5,7,4,2,1,3]=>0000000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[7,1,4,5,6,2,8,3]=>[2,8,5,4,3,7,1,6]=>[5,8,2,7,4,3,1,6]=>0000000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[6,8,5,4,3,1,7,2]=>[6,5,8,7,4,3,1,2]=>0000000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>[1,8,5,4,3,2,7,6]=>[5,1,8,7,4,3,2,6]=>0000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[6,8,5,4,3,2,1,7]=>[6,8,5,4,3,2,1,7]=>0000000
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[7,2,8,6,5,4,1,3]=>[7,8,6,5,2,1,4,3]=>0000000
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,8,1,6,3,7,4,5]=>[7,1,8,3,6,2,5,4]=>[7,6,8,1,3,2,5,4]=>0000000
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,6,1,5,3,7,8,4]=>[7,3,8,4,6,2,1,5]=>[7,8,3,2,4,1,6,5]=>0000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,6,1,2,3,4,8,5]=>[2,3,8,7,6,5,1,4]=>[2,8,7,6,5,1,3,4]=>0000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,1,2,3,7,8,4]=>[4,3,8,7,6,2,1,5]=>[4,8,7,3,2,1,6,5]=>0000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7,4,1,2,6,3,8,5]=>[2,5,8,7,3,6,1,4]=>[5,8,2,7,6,1,3,4]=>0000000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8,4,1,2,6,7,3,5]=>[1,5,8,7,3,2,6,4]=>[5,3,8,7,6,1,2,4]=>0000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,1,2,6,7,8,3]=>[4,5,8,7,3,2,1,6]=>[4,8,7,3,2,1,5,6]=>0000000
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,3,1,6,2,8,5,7]=>[5,6,8,3,7,1,4,2]=>[8,5,6,3,4,1,2,7]=>0000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>[1,6,8,4,7,2,5,3]=>[8,6,7,4,5,1,2,3]=>0000000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>[2,5,8,4,7,6,1,3]=>[5,8,7,2,4,1,3,6]=>0000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7,4,1,6,2,3,8,5]=>[2,5,8,3,7,6,1,4]=>[5,8,7,2,6,1,3,4]=>0000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[8,7,1,5,2,3,4,6]=>[1,2,8,4,7,6,5,3]=>[8,7,6,1,4,2,3,5]=>0000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>[1,2,8,3,7,6,5,4]=>[8,7,6,1,5,2,3,4]=>0000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,8,1,5,2,7,3,4]=>[3,1,8,4,7,2,6,5]=>[8,3,7,1,4,2,6,5]=>0000000
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,1,8,6,2,5,7]=>[5,6,8,1,3,7,4,2]=>[8,5,3,6,7,1,2,4]=>0000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>[1,6,8,4,2,7,5,3]=>[8,6,4,7,5,1,2,3]=>0000000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>[1,6,8,2,3,7,5,4]=>[8,6,1,5,7,2,3,4]=>0000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7,3,1,5,6,2,8,4]=>[2,6,8,4,3,7,1,5]=>[6,8,4,7,2,1,3,5]=>0000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[8,4,1,5,7,2,3,6]=>[1,5,8,4,2,7,6,3]=>[8,5,4,7,6,1,2,3]=>0000000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,7,1,6,4,8,5]=>[7,6,2,8,3,5,1,4]=>[7,8,2,3,1,6,5,4]=>0000000
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]=>[7,6,4,8,1,2,5,3]=>[7,1,4,8,2,6,5,3]=>0000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]=>[7,3,5,8,6,1,4,2]=>[7,5,8,3,1,4,6,2]=>0000000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]=>[7,3,5,8,6,2,1,4]=>[7,8,3,2,1,5,6,4]=>0000000
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[7,3,2,8,6,5,1,4]=>[7,8,3,2,1,6,5,4]=>0000000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]=>[7,3,4,8,6,2,1,5]=>[7,8,3,2,1,4,6,5]=>0000000
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,1,8,7,3,6]=>[7,4,5,8,1,2,6,3]=>[7,4,5,8,1,2,6,3]=>0000000
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,8,4,1,6,7,3,5]=>[7,1,5,8,3,2,6,4]=>[7,5,8,6,1,3,4,2]=>0000000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>[2,6,4,8,7,5,1,3]=>[6,8,7,2,1,4,3,5]=>0000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>[8,7,6,4,1,2,3,5]=>0000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]=>[8,7,3,2,1,6,5,4]=>0000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>[1,4,5,8,7,2,6,3]=>[8,4,7,5,1,2,3,6]=>0000000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,3,4,1,8,2,6,7]=>[4,6,5,8,1,7,3,2]=>[6,4,3,8,1,5,2,7]=>0000000
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,3,4,1,7,2,5,6]=>[1,6,5,8,2,7,4,3]=>[6,5,4,8,1,7,2,3]=>0000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7,3,4,1,6,2,8,5]=>[2,6,5,8,3,7,1,4]=>[6,8,5,7,2,3,1,4]=>0000000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[8,3,5,1,7,2,4,6]=>[1,6,4,8,2,7,5,3]=>[8,6,4,7,1,5,2,3]=>0000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,3,5,1,6,2,8,4]=>[2,6,4,8,3,7,1,5]=>[6,8,4,7,2,3,1,5]=>0000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>[2,1,5,8,3,7,6,4]=>[8,7,2,5,1,3,6,4]=>0000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[8,5,4,1,6,7,2,3]=>[1,4,5,8,3,2,7,6]=>[4,3,8,7,1,2,5,6]=>0000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]=>[7,6,5,1,8,4,3,2]=>0000000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,6,1,4,8,5]=>[7,6,2,3,8,5,1,4]=>[7,8,2,1,3,6,5,4]=>0000000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,6,5,1,7,8,4]=>[7,6,3,4,8,2,1,5]=>[7,8,6,3,4,5,2,1]=>0000000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,8,4,6,1,3,5,7]=>[7,1,5,3,8,6,4,2]=>[7,5,3,1,8,2,6,4]=>0000000
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,8,4,5,1,7,3,6]=>[7,1,5,4,8,2,6,3]=>[7,5,8,1,6,2,4,3]=>0000000
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,8,4,6,1,7,3,5]=>[7,1,5,3,8,2,6,4]=>[7,5,8,1,6,3,4,2]=>0000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>[2,1,3,4,8,7,6,5]=>[8,7,2,1,3,4,6,5]=>0000000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,4,8,7,1,5,6]=>[7,6,5,1,2,8,4,3]=>[7,6,1,2,8,5,4,3]=>0000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,8,4,7,6,1,3,5]=>[7,1,5,2,3,8,6,4]=>[7,5,1,2,8,3,6,4]=>0000000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[1,6,5,4,3,8,7,2]=>[6,5,1,8,4,3,2,7]=>0000000
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
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