Identifier
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>0 [1,0,1,0]=>[1,2]=>0 [1,1,0,0]=>[2,1]=>1 [1,0,1,0,1,0]=>[1,2,3]=>0 [1,0,1,1,0,0]=>[1,3,2]=>1 [1,1,0,0,1,0]=>[2,1,3]=>1 [1,1,0,1,0,0]=>[2,3,1]=>2 [1,1,1,0,0,0]=>[3,1,2]=>2 [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>0 [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>1 [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>1 [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>2 [1,0,1,1,1,0,0,0]=>[1,4,2,3]=>2 [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>1 [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>2 [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>2 [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>3 [1,1,0,1,1,0,0,0]=>[2,4,1,3]=>3 [1,1,1,0,0,0,1,0]=>[3,1,2,4]=>2 [1,1,1,0,0,1,0,0]=>[3,1,4,2]=>3 [1,1,1,0,1,0,0,0]=>[3,4,1,2]=>4 [1,1,1,1,0,0,0,0]=>[4,1,2,3]=>3 [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>0 [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>1 [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>1 [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>2 [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>2 [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>1 [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>2 [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>2 [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>3 [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>3 [1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>2 [1,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3]=>3 [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,2,3]=>4 [1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>3 [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>1 [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>2 [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>2 [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>3 [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>3 [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>2 [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>3 [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>3 [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>4 [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>4 [1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,5]=>3 [1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,3]=>4 [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,3]=>5 [1,1,0,1,1,1,0,0,0,0]=>[2,5,1,3,4]=>4 [1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>2 [1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>3 [1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,5]=>3 [1,1,1,0,0,1,0,1,0,0]=>[3,1,4,5,2]=>4 [1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4]=>4 [1,1,1,0,1,0,0,0,1,0]=>[3,4,1,2,5]=>4 [1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,2]=>5 [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,2]=>6 [1,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4]=>5 [1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>3 [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,3]=>4 [1,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,3]=>5 [1,1,1,1,0,1,0,0,0,0]=>[4,5,1,2,3]=>6 [1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>4 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>0 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>1 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>1 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>2 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>2 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>1 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>2 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>2 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>3 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5]=>3 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>2 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,3,6,4]=>3 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,3,4]=>4 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>3 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>1 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>2 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>2 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>3 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>3 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>2 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>3 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>3 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>4 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,2,5]=>4 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,6]=>3 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,6,4]=>4 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,2,4]=>5 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,2,4,5]=>4 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>2 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>3 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3,6]=>3 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,6,3]=>4 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5]=>4 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,2,3,6]=>4 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,2,6,3]=>5 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,2,3]=>6 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5]=>5 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>3 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,4]=>4 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,2,6,3,4]=>5 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,2,3,4]=>6 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>4 [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>1 [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>2 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>2 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>3 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>3 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>2 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>3 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>3 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>4 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5]=>4 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>3 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,6,4]=>4 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,3,4]=>5 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>4 [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>2 [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>3 [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>3 [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>4 [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,4,5]=>4 [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>3 [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>4 [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>4 [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>5 [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,1,5]=>5 [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,6]=>4 [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,6,4]=>5 [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,1,4]=>6 [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,1,4,5]=>5 [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,5,6]=>3 [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5]=>4 [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,5,3,6]=>4 [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,6,3]=>5 [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5]=>5 [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,1,3,6]=>5 [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,1,6,3]=>6 [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,1,3]=>7 [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5]=>6 [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,6]=>4 [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,4]=>5 [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,1,6,3,4]=>6 [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,1,3,4]=>7 [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,3,4,5]=>5 [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>2 [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>3 [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>3 [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,6,4]=>4 [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>4 [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>3 [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,2,6,5]=>4 [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>4 [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,2]=>5 [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,4,6,2,5]=>5 [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,6]=>4 [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,6,4]=>5 [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,6,2,4]=>6 [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,2,4,5]=>5 [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,1,2,5,6]=>4 [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5]=>5 [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,1,5,2,6]=>5 [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,6,2]=>6 [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5]=>6 [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,1,2,6]=>6 [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,1,6,2]=>7 [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,1,2]=>8 [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5]=>7 [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,6]=>5 [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,6,4]=>6 [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,6,2,4]=>7 [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,1,2,4]=>8 [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,1,2,4,5]=>6 [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>3 [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>4 [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>4 [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,3]=>5 [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5]=>5 [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,5,2,3,6]=>5 [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,5,2,6,3]=>6 [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,5,6,2,3]=>7 [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5]=>6 [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,1,2,3,6]=>6 [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,1,2,6,3]=>7 [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,1,6,2,3]=>8 [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,1,2,3]=>9 [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5]=>7 [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>4 [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,6,4]=>5 [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,6,3,4]=>6 [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1,6,2,3,4]=>7 [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,1,2,3,4]=>8 [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>5 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>0 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>1 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>1 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>2 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>2 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>1 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>2 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>2 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>3 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6]=>3 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>2 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,4,7,5]=>3 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,4,5]=>4 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>3 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>1 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>2 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>2 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>3 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>3 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>2 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>3 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>3 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>4 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6]=>4 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,7]=>3 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,7,5]=>4 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,3,5]=>5 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>4 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>2 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>3 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,6,4,7]=>3 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,6,7,4]=>4 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6]=>4 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,3,4,7]=>4 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,3,7,4]=>5 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,3,4]=>6 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>5 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>3 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,7,5]=>4 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>5 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>6 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>4 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>1 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>2 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>2 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>3 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>3 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>2 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>3 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>3 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>4 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6]=>4 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>3 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,7,5]=>4 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,4,5]=>5 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>4 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>2 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>3 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>3 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>4 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,5,6]=>4 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>3 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>4 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>4 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>5 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6]=>5 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,7]=>4 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,7,5]=>5 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,2,5]=>6 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>5 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,6,7]=>3 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6]=>4 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,6,4,7]=>4 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,6,7,4]=>5 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6]=>5 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,2,4,7]=>5 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,2,7,4]=>6 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,2,4]=>7 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>6 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,7]=>4 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,7,5]=>5 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>6 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>7 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6]=>5 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>2 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>3 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>3 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,7,5]=>4 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>4 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,3,6,7]=>3 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6]=>4 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,3,7]=>4 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,3]=>5 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6]=>5 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,7]=>4 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,7,5]=>5 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,7,3,5]=>6 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,7,3,5,6]=>5 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,6,7]=>4 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6]=>5 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,2,6,3,7]=>5 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,2,6,7,3]=>6 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6]=>6 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,2,3,7]=>6 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,2,7,3]=>7 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,2,3]=>8 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>7 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,7]=>5 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,7,5]=>6 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>7
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Description
The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation.
This is for a permutation $\sigma$ of length $n$ and the set $T = \{ (1,2), \dots, (n-1,n), (1,n) \}$ given by
$$\min\{ k \mid \sigma = t_1\dots t_k \text{ for } t_i \in T \text{ such that } t_1\dots t_j \text{ has more cyclic descents than } t_1\dots t_{j-1} \text{ for all } j\}.$$
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.