Identifier
Identifier
Mp00114: Permutations connectivity setBinary words
Images
[1] =>
[1,2] => 1
[2,1] => 0
[1,2,3] => 11
[1,3,2] => 10
[2,1,3] => 01
[2,3,1] => 00
[3,1,2] => 00
[3,2,1] => 00
[1,2,3,4] => 111
[1,2,4,3] => 110
[1,3,2,4] => 101
[1,3,4,2] => 100
[1,4,2,3] => 100
[1,4,3,2] => 100
[2,1,3,4] => 011
[2,1,4,3] => 010
[2,3,1,4] => 001
[2,3,4,1] => 000
[2,4,1,3] => 000
[2,4,3,1] => 000
[3,1,2,4] => 001
[3,1,4,2] => 000
[3,2,1,4] => 001
[3,2,4,1] => 000
[3,4,1,2] => 000
[3,4,2,1] => 000
[4,1,2,3] => 000
[4,1,3,2] => 000
[4,2,1,3] => 000
[4,2,3,1] => 000
[4,3,1,2] => 000
[4,3,2,1] => 000
[1,2,3,4,5] => 1111
[1,2,3,5,4] => 1110
[1,2,4,3,5] => 1101
[1,2,4,5,3] => 1100
[1,2,5,3,4] => 1100
[1,2,5,4,3] => 1100
[1,3,2,4,5] => 1011
[1,3,2,5,4] => 1010
[1,3,4,2,5] => 1001
[1,3,4,5,2] => 1000
[1,3,5,2,4] => 1000
[1,3,5,4,2] => 1000
[1,4,2,3,5] => 1001
[1,4,2,5,3] => 1000
[1,4,3,2,5] => 1001
[1,4,3,5,2] => 1000
[1,4,5,2,3] => 1000
[1,4,5,3,2] => 1000
[1,5,2,3,4] => 1000
[1,5,2,4,3] => 1000
[1,5,3,2,4] => 1000
[1,5,3,4,2] => 1000
[1,5,4,2,3] => 1000
[1,5,4,3,2] => 1000
[2,1,3,4,5] => 0111
[2,1,3,5,4] => 0110
[2,1,4,3,5] => 0101
[2,1,4,5,3] => 0100
[2,1,5,3,4] => 0100
[2,1,5,4,3] => 0100
[2,3,1,4,5] => 0011
[2,3,1,5,4] => 0010
[2,3,4,1,5] => 0001
[2,3,4,5,1] => 0000
[2,3,5,1,4] => 0000
[2,3,5,4,1] => 0000
[2,4,1,3,5] => 0001
[2,4,1,5,3] => 0000
[2,4,3,1,5] => 0001
[2,4,3,5,1] => 0000
[2,4,5,1,3] => 0000
[2,4,5,3,1] => 0000
[2,5,1,3,4] => 0000
[2,5,1,4,3] => 0000
[2,5,3,1,4] => 0000
[2,5,3,4,1] => 0000
[2,5,4,1,3] => 0000
[2,5,4,3,1] => 0000
[3,1,2,4,5] => 0011
[3,1,2,5,4] => 0010
[3,1,4,2,5] => 0001
[3,1,4,5,2] => 0000
[3,1,5,2,4] => 0000
[3,1,5,4,2] => 0000
[3,2,1,4,5] => 0011
[3,2,1,5,4] => 0010
[3,2,4,1,5] => 0001
[3,2,4,5,1] => 0000
[3,2,5,1,4] => 0000
[3,2,5,4,1] => 0000
[3,4,1,2,5] => 0001
[3,4,1,5,2] => 0000
[3,4,2,1,5] => 0001
[3,4,2,5,1] => 0000
[3,4,5,1,2] => 0000
[3,4,5,2,1] => 0000
[3,5,1,2,4] => 0000
[3,5,1,4,2] => 0000
[3,5,2,1,4] => 0000
[3,5,2,4,1] => 0000
[3,5,4,1,2] => 0000
[3,5,4,2,1] => 0000
[4,1,2,3,5] => 0001
[4,1,2,5,3] => 0000
[4,1,3,2,5] => 0001
[4,1,3,5,2] => 0000
[4,1,5,2,3] => 0000
[4,1,5,3,2] => 0000
[4,2,1,3,5] => 0001
[4,2,1,5,3] => 0000
[4,2,3,1,5] => 0001
[4,2,3,5,1] => 0000
[4,2,5,1,3] => 0000
[4,2,5,3,1] => 0000
[4,3,1,2,5] => 0001
[4,3,1,5,2] => 0000
[4,3,2,1,5] => 0001
[4,3,2,5,1] => 0000
[4,3,5,1,2] => 0000
[4,3,5,2,1] => 0000
[4,5,1,2,3] => 0000
[4,5,1,3,2] => 0000
[4,5,2,1,3] => 0000
[4,5,2,3,1] => 0000
[4,5,3,1,2] => 0000
[4,5,3,2,1] => 0000
[5,1,2,3,4] => 0000
[5,1,2,4,3] => 0000
[5,1,3,2,4] => 0000
[5,1,3,4,2] => 0000
[5,1,4,2,3] => 0000
[5,1,4,3,2] => 0000
[5,2,1,3,4] => 0000
[5,2,1,4,3] => 0000
[5,2,3,1,4] => 0000
[5,2,3,4,1] => 0000
[5,2,4,1,3] => 0000
[5,2,4,3,1] => 0000
[5,3,1,2,4] => 0000
[5,3,1,4,2] => 0000
[5,3,2,1,4] => 0000
[5,3,2,4,1] => 0000
[5,3,4,1,2] => 0000
[5,3,4,2,1] => 0000
[5,4,1,2,3] => 0000
[5,4,1,3,2] => 0000
[5,4,2,1,3] => 0000
[5,4,2,3,1] => 0000
[5,4,3,1,2] => 0000
[5,4,3,2,1] => 0000
[1,2,3,4,5,6] => 11111
[1,2,3,4,6,5] => 11110
[1,2,3,5,4,6] => 11101
[1,2,3,5,6,4] => 11100
[1,2,3,6,4,5] => 11100
[1,2,3,6,5,4] => 11100
[1,2,4,3,5,6] => 11011
[1,2,4,3,6,5] => 11010
[1,2,4,5,3,6] => 11001
[1,2,4,5,6,3] => 11000
[1,2,4,6,3,5] => 11000
[1,2,4,6,5,3] => 11000
[1,2,5,3,4,6] => 11001
[1,2,5,3,6,4] => 11000
[1,2,5,4,3,6] => 11001
[1,2,5,4,6,3] => 11000
[1,2,5,6,3,4] => 11000
[1,2,5,6,4,3] => 11000
[1,2,6,3,4,5] => 11000
[1,2,6,3,5,4] => 11000
[1,2,6,4,3,5] => 11000
[1,2,6,4,5,3] => 11000
[1,2,6,5,3,4] => 11000
[1,2,6,5,4,3] => 11000
[1,3,2,4,5,6] => 10111
[1,3,2,4,6,5] => 10110
[1,3,2,5,4,6] => 10101
[1,3,2,5,6,4] => 10100
[1,3,2,6,4,5] => 10100
[1,3,2,6,5,4] => 10100
[1,3,4,2,5,6] => 10011
[1,3,4,2,6,5] => 10010
[1,3,4,5,2,6] => 10001
[1,3,4,5,6,2] => 10000
[1,3,4,6,2,5] => 10000
[1,3,4,6,5,2] => 10000
[1,3,5,2,4,6] => 10001
[1,3,5,2,6,4] => 10000
[1,3,5,4,2,6] => 10001
[1,3,5,4,6,2] => 10000
[1,3,5,6,2,4] => 10000
[1,3,5,6,4,2] => 10000
[1,3,6,2,4,5] => 10000
[1,3,6,2,5,4] => 10000
[1,3,6,4,2,5] => 10000
[1,3,6,4,5,2] => 10000
[1,3,6,5,2,4] => 10000
[1,3,6,5,4,2] => 10000
[1,4,2,3,5,6] => 10011
[1,4,2,3,6,5] => 10010
[1,4,2,5,3,6] => 10001
[1,4,2,5,6,3] => 10000
[1,4,2,6,3,5] => 10000
[1,4,2,6,5,3] => 10000
[1,4,3,2,5,6] => 10011
[1,4,3,2,6,5] => 10010
[1,4,3,5,2,6] => 10001
[1,4,3,5,6,2] => 10000
[1,4,3,6,2,5] => 10000
[1,4,3,6,5,2] => 10000
[1,4,5,2,3,6] => 10001
[1,4,5,2,6,3] => 10000
[1,4,5,3,2,6] => 10001
[1,4,5,3,6,2] => 10000
[1,4,5,6,2,3] => 10000
[1,4,5,6,3,2] => 10000
[1,4,6,2,3,5] => 10000
[1,4,6,2,5,3] => 10000
[1,4,6,3,2,5] => 10000
[1,4,6,3,5,2] => 10000
[1,4,6,5,2,3] => 10000
[1,4,6,5,3,2] => 10000
[1,5,2,3,4,6] => 10001
[1,5,2,3,6,4] => 10000
[1,5,2,4,3,6] => 10001
[1,5,2,4,6,3] => 10000
[1,5,2,6,3,4] => 10000
[1,5,2,6,4,3] => 10000
[1,5,3,2,4,6] => 10001
[1,5,3,2,6,4] => 10000
[1,5,3,4,2,6] => 10001
[1,5,3,4,6,2] => 10000
[1,5,3,6,2,4] => 10000
[1,5,3,6,4,2] => 10000
[1,5,4,2,3,6] => 10001
[1,5,4,2,6,3] => 10000
[1,5,4,3,2,6] => 10001
[1,5,4,3,6,2] => 10000
[1,5,4,6,2,3] => 10000
[1,5,4,6,3,2] => 10000
[1,5,6,2,3,4] => 10000
[1,5,6,2,4,3] => 10000
[1,5,6,3,2,4] => 10000
[1,5,6,3,4,2] => 10000
[1,5,6,4,2,3] => 10000
[1,5,6,4,3,2] => 10000
[1,6,2,3,4,5] => 10000
[1,6,2,3,5,4] => 10000
[1,6,2,4,3,5] => 10000
[1,6,2,4,5,3] => 10000
[1,6,2,5,3,4] => 10000
[1,6,2,5,4,3] => 10000
[1,6,3,2,4,5] => 10000
[1,6,3,2,5,4] => 10000
[1,6,3,4,2,5] => 10000
[1,6,3,4,5,2] => 10000
[1,6,3,5,2,4] => 10000
[1,6,3,5,4,2] => 10000
[1,6,4,2,3,5] => 10000
[1,6,4,2,5,3] => 10000
[1,6,4,3,2,5] => 10000
[1,6,4,3,5,2] => 10000
[1,6,4,5,2,3] => 10000
[1,6,4,5,3,2] => 10000
[1,6,5,2,3,4] => 10000
[1,6,5,2,4,3] => 10000
[1,6,5,3,2,4] => 10000
[1,6,5,3,4,2] => 10000
[1,6,5,4,2,3] => 10000
[1,6,5,4,3,2] => 10000
[2,1,3,4,5,6] => 01111
[2,1,3,4,6,5] => 01110
[2,1,3,5,4,6] => 01101
[2,1,3,5,6,4] => 01100
[2,1,3,6,4,5] => 01100
[2,1,3,6,5,4] => 01100
[2,1,4,3,5,6] => 01011
[2,1,4,3,6,5] => 01010
[2,1,4,5,3,6] => 01001
[2,1,4,5,6,3] => 01000
[2,1,4,6,3,5] => 01000
[2,1,4,6,5,3] => 01000
[2,1,5,3,4,6] => 01001
[2,1,5,3,6,4] => 01000
[2,1,5,4,3,6] => 01001
[2,1,5,4,6,3] => 01000
[2,1,5,6,3,4] => 01000
[2,1,5,6,4,3] => 01000
[2,1,6,3,4,5] => 01000
[2,1,6,3,5,4] => 01000
[2,1,6,4,3,5] => 01000
[2,1,6,4,5,3] => 01000
[2,1,6,5,3,4] => 01000
[2,1,6,5,4,3] => 01000
[2,3,1,4,5,6] => 00111
[2,3,1,4,6,5] => 00110
[2,3,1,5,4,6] => 00101
[2,3,1,5,6,4] => 00100
[2,3,1,6,4,5] => 00100
[2,3,1,6,5,4] => 00100
[2,3,4,1,5,6] => 00011
[2,3,4,1,6,5] => 00010
[2,3,4,5,1,6] => 00001
[2,3,4,5,6,1] => 00000
[2,3,4,6,1,5] => 00000
[2,3,4,6,5,1] => 00000
[2,3,5,1,4,6] => 00001
[2,3,5,1,6,4] => 00000
[2,3,5,4,1,6] => 00001
[2,3,5,4,6,1] => 00000
[2,3,5,6,1,4] => 00000
[2,3,5,6,4,1] => 00000
[2,3,6,1,4,5] => 00000
[2,3,6,1,5,4] => 00000
[2,3,6,4,1,5] => 00000
[2,3,6,4,5,1] => 00000
[2,3,6,5,1,4] => 00000
[2,3,6,5,4,1] => 00000
[2,4,1,3,5,6] => 00011
[2,4,1,3,6,5] => 00010
[2,4,1,5,3,6] => 00001
[2,4,1,5,6,3] => 00000
[2,4,1,6,3,5] => 00000
[2,4,1,6,5,3] => 00000
[2,4,3,1,5,6] => 00011
[2,4,3,1,6,5] => 00010
[2,4,3,5,1,6] => 00001
[2,4,3,5,6,1] => 00000
[2,4,3,6,1,5] => 00000
[2,4,3,6,5,1] => 00000
[2,4,5,1,3,6] => 00001
[2,4,5,1,6,3] => 00000
[2,4,5,3,1,6] => 00001
[2,4,5,3,6,1] => 00000
[2,4,5,6,1,3] => 00000
[2,4,5,6,3,1] => 00000
[2,4,6,1,3,5] => 00000
[2,4,6,1,5,3] => 00000
[2,4,6,3,1,5] => 00000
[2,4,6,3,5,1] => 00000
[2,4,6,5,1,3] => 00000
[2,4,6,5,3,1] => 00000
[2,5,1,3,4,6] => 00001
[2,5,1,3,6,4] => 00000
[2,5,1,4,3,6] => 00001
[2,5,1,4,6,3] => 00000
[2,5,1,6,3,4] => 00000
[2,5,1,6,4,3] => 00000
[2,5,3,1,4,6] => 00001
[2,5,3,1,6,4] => 00000
[2,5,3,4,1,6] => 00001
[2,5,3,4,6,1] => 00000
[2,5,3,6,1,4] => 00000
[2,5,3,6,4,1] => 00000
[2,5,4,1,3,6] => 00001
[2,5,4,1,6,3] => 00000
[2,5,4,3,1,6] => 00001
[2,5,4,3,6,1] => 00000
[2,5,4,6,1,3] => 00000
[2,5,4,6,3,1] => 00000
[2,5,6,1,3,4] => 00000
[2,5,6,1,4,3] => 00000
[2,5,6,3,1,4] => 00000
[2,5,6,3,4,1] => 00000
[2,5,6,4,1,3] => 00000
[2,5,6,4,3,1] => 00000
[2,6,1,3,4,5] => 00000
[2,6,1,3,5,4] => 00000
[2,6,1,4,3,5] => 00000
[2,6,1,4,5,3] => 00000
[2,6,1,5,3,4] => 00000
[2,6,1,5,4,3] => 00000
[2,6,3,1,4,5] => 00000
[2,6,3,1,5,4] => 00000
[2,6,3,4,1,5] => 00000
[2,6,3,4,5,1] => 00000
[2,6,3,5,1,4] => 00000
[2,6,3,5,4,1] => 00000
[2,6,4,1,3,5] => 00000
[2,6,4,1,5,3] => 00000
[2,6,4,3,1,5] => 00000
[2,6,4,3,5,1] => 00000
[2,6,4,5,1,3] => 00000
[2,6,4,5,3,1] => 00000
[2,6,5,1,3,4] => 00000
[2,6,5,1,4,3] => 00000
[2,6,5,3,1,4] => 00000
[2,6,5,3,4,1] => 00000
[2,6,5,4,1,3] => 00000
[2,6,5,4,3,1] => 00000
[3,1,2,4,5,6] => 00111
[3,1,2,4,6,5] => 00110
[3,1,2,5,4,6] => 00101
[3,1,2,5,6,4] => 00100
[3,1,2,6,4,5] => 00100
[3,1,2,6,5,4] => 00100
[3,1,4,2,5,6] => 00011
[3,1,4,2,6,5] => 00010
[3,1,4,5,2,6] => 00001
[3,1,4,5,6,2] => 00000
[3,1,4,6,2,5] => 00000
[3,1,4,6,5,2] => 00000
[3,1,5,2,4,6] => 00001
[3,1,5,2,6,4] => 00000
[3,1,5,4,2,6] => 00001
[3,1,5,4,6,2] => 00000
[3,1,5,6,2,4] => 00000
[3,1,5,6,4,2] => 00000
[3,1,6,2,4,5] => 00000
[3,1,6,2,5,4] => 00000
[3,1,6,4,2,5] => 00000
[3,1,6,4,5,2] => 00000
[3,1,6,5,2,4] => 00000
[3,1,6,5,4,2] => 00000
[3,2,1,4,5,6] => 00111
[3,2,1,4,6,5] => 00110
[3,2,1,5,4,6] => 00101
[3,2,1,5,6,4] => 00100
[3,2,1,6,4,5] => 00100
[3,2,1,6,5,4] => 00100
[3,2,4,1,5,6] => 00011
[3,2,4,1,6,5] => 00010
[3,2,4,5,1,6] => 00001
[3,2,4,5,6,1] => 00000
[3,2,4,6,1,5] => 00000
[3,2,4,6,5,1] => 00000
[3,2,5,1,4,6] => 00001
[3,2,5,1,6,4] => 00000
[3,2,5,4,1,6] => 00001
[3,2,5,4,6,1] => 00000
[3,2,5,6,1,4] => 00000
[3,2,5,6,4,1] => 00000
[3,2,6,1,4,5] => 00000
[3,2,6,1,5,4] => 00000
[3,2,6,4,1,5] => 00000
[3,2,6,4,5,1] => 00000
[3,2,6,5,1,4] => 00000
[3,2,6,5,4,1] => 00000
[3,4,1,2,5,6] => 00011
[3,4,1,2,6,5] => 00010
[3,4,1,5,2,6] => 00001
[3,4,1,5,6,2] => 00000
[3,4,1,6,2,5] => 00000
[3,4,1,6,5,2] => 00000
[3,4,2,1,5,6] => 00011
[3,4,2,1,6,5] => 00010
[3,4,2,5,1,6] => 00001
[3,4,2,5,6,1] => 00000
[3,4,2,6,1,5] => 00000
[3,4,2,6,5,1] => 00000
[3,4,5,1,2,6] => 00001
[3,4,5,1,6,2] => 00000
[3,4,5,2,1,6] => 00001
[3,4,5,2,6,1] => 00000
[3,4,5,6,1,2] => 00000
[3,4,5,6,2,1] => 00000
[3,4,6,1,2,5] => 00000
[3,4,6,1,5,2] => 00000
[3,4,6,2,1,5] => 00000
[3,4,6,2,5,1] => 00000
[3,4,6,5,1,2] => 00000
[3,4,6,5,2,1] => 00000
[3,5,1,2,4,6] => 00001
[3,5,1,2,6,4] => 00000
[3,5,1,4,2,6] => 00001
[3,5,1,4,6,2] => 00000
[3,5,1,6,2,4] => 00000
[3,5,1,6,4,2] => 00000
[3,5,2,1,4,6] => 00001
[3,5,2,1,6,4] => 00000
[3,5,2,4,1,6] => 00001
[3,5,2,4,6,1] => 00000
[3,5,2,6,1,4] => 00000
[3,5,2,6,4,1] => 00000
[3,5,4,1,2,6] => 00001
[3,5,4,1,6,2] => 00000
[3,5,4,2,1,6] => 00001
[3,5,4,2,6,1] => 00000
[3,5,4,6,1,2] => 00000
[3,5,4,6,2,1] => 00000
[3,5,6,1,2,4] => 00000
[3,5,6,1,4,2] => 00000
[3,5,6,2,1,4] => 00000
[3,5,6,2,4,1] => 00000
[3,5,6,4,1,2] => 00000
[3,5,6,4,2,1] => 00000
[3,6,1,2,4,5] => 00000
[3,6,1,2,5,4] => 00000
[3,6,1,4,2,5] => 00000
[3,6,1,4,5,2] => 00000
[3,6,1,5,2,4] => 00000
[3,6,1,5,4,2] => 00000
[3,6,2,1,4,5] => 00000
[3,6,2,1,5,4] => 00000
[3,6,2,4,1,5] => 00000
[3,6,2,4,5,1] => 00000
[3,6,2,5,1,4] => 00000
[3,6,2,5,4,1] => 00000
[3,6,4,1,2,5] => 00000
[3,6,4,1,5,2] => 00000
[3,6,4,2,1,5] => 00000
[3,6,4,2,5,1] => 00000
[3,6,4,5,1,2] => 00000
[3,6,4,5,2,1] => 00000
[3,6,5,1,2,4] => 00000
[3,6,5,1,4,2] => 00000
[3,6,5,2,1,4] => 00000
[3,6,5,2,4,1] => 00000
[3,6,5,4,1,2] => 00000
[3,6,5,4,2,1] => 00000
[4,1,2,3,5,6] => 00011
[4,1,2,3,6,5] => 00010
[4,1,2,5,3,6] => 00001
[4,1,2,5,6,3] => 00000
[4,1,2,6,3,5] => 00000
[4,1,2,6,5,3] => 00000
[4,1,3,2,5,6] => 00011
[4,1,3,2,6,5] => 00010
[4,1,3,5,2,6] => 00001
[4,1,3,5,6,2] => 00000
[4,1,3,6,2,5] => 00000
[4,1,3,6,5,2] => 00000
[4,1,5,2,3,6] => 00001
[4,1,5,2,6,3] => 00000
[4,1,5,3,2,6] => 00001
[4,1,5,3,6,2] => 00000
[4,1,5,6,2,3] => 00000
[4,1,5,6,3,2] => 00000
[4,1,6,2,3,5] => 00000
[4,1,6,2,5,3] => 00000
[4,1,6,3,2,5] => 00000
[4,1,6,3,5,2] => 00000
[4,1,6,5,2,3] => 00000
[4,1,6,5,3,2] => 00000
[4,2,1,3,5,6] => 00011
[4,2,1,3,6,5] => 00010
[4,2,1,5,3,6] => 00001
[4,2,1,5,6,3] => 00000
[4,2,1,6,3,5] => 00000
[4,2,1,6,5,3] => 00000
[4,2,3,1,5,6] => 00011
[4,2,3,1,6,5] => 00010
[4,2,3,5,1,6] => 00001
[4,2,3,5,6,1] => 00000
[4,2,3,6,1,5] => 00000
[4,2,3,6,5,1] => 00000
[4,2,5,1,3,6] => 00001
[4,2,5,1,6,3] => 00000
[4,2,5,3,1,6] => 00001
[4,2,5,3,6,1] => 00000
[4,2,5,6,1,3] => 00000
[4,2,5,6,3,1] => 00000
[4,2,6,1,3,5] => 00000
[4,2,6,1,5,3] => 00000
[4,2,6,3,1,5] => 00000
[4,2,6,3,5,1] => 00000
[4,2,6,5,1,3] => 00000
[4,2,6,5,3,1] => 00000
[4,3,1,2,5,6] => 00011
[4,3,1,2,6,5] => 00010
[4,3,1,5,2,6] => 00001
[4,3,1,5,6,2] => 00000
[4,3,1,6,2,5] => 00000
[4,3,1,6,5,2] => 00000
[4,3,2,1,5,6] => 00011
[4,3,2,1,6,5] => 00010
[4,3,2,5,1,6] => 00001
[4,3,2,5,6,1] => 00000
[4,3,2,6,1,5] => 00000
[4,3,2,6,5,1] => 00000
[4,3,5,1,2,6] => 00001
[4,3,5,1,6,2] => 00000
[4,3,5,2,1,6] => 00001
[4,3,5,2,6,1] => 00000
[4,3,5,6,1,2] => 00000
[4,3,5,6,2,1] => 00000
[4,3,6,1,2,5] => 00000
[4,3,6,1,5,2] => 00000
[4,3,6,2,1,5] => 00000
[4,3,6,2,5,1] => 00000
[4,3,6,5,1,2] => 00000
[4,3,6,5,2,1] => 00000
[4,5,1,2,3,6] => 00001
[4,5,1,2,6,3] => 00000
[4,5,1,3,2,6] => 00001
[4,5,1,3,6,2] => 00000
[4,5,1,6,2,3] => 00000
[4,5,1,6,3,2] => 00000
[4,5,2,1,3,6] => 00001
[4,5,2,1,6,3] => 00000
[4,5,2,3,1,6] => 00001
[4,5,2,3,6,1] => 00000
[4,5,2,6,1,3] => 00000
[4,5,2,6,3,1] => 00000
[4,5,3,1,2,6] => 00001
[4,5,3,1,6,2] => 00000
[4,5,3,2,1,6] => 00001
[4,5,3,2,6,1] => 00000
[4,5,3,6,1,2] => 00000
[4,5,3,6,2,1] => 00000
[4,5,6,1,2,3] => 00000
[4,5,6,1,3,2] => 00000
[4,5,6,2,1,3] => 00000
[4,5,6,2,3,1] => 00000
[4,5,6,3,1,2] => 00000
[4,5,6,3,2,1] => 00000
[4,6,1,2,3,5] => 00000
[4,6,1,2,5,3] => 00000
[4,6,1,3,2,5] => 00000
[4,6,1,3,5,2] => 00000
[4,6,1,5,2,3] => 00000
[4,6,1,5,3,2] => 00000
[4,6,2,1,3,5] => 00000
[4,6,2,1,5,3] => 00000
[4,6,2,3,1,5] => 00000
[4,6,2,3,5,1] => 00000
[4,6,2,5,1,3] => 00000
[4,6,2,5,3,1] => 00000
[4,6,3,1,2,5] => 00000
[4,6,3,1,5,2] => 00000
[4,6,3,2,1,5] => 00000
[4,6,3,2,5,1] => 00000
[4,6,3,5,1,2] => 00000
[4,6,3,5,2,1] => 00000
[4,6,5,1,2,3] => 00000
[4,6,5,1,3,2] => 00000
[4,6,5,2,1,3] => 00000
[4,6,5,2,3,1] => 00000
[4,6,5,3,1,2] => 00000
[4,6,5,3,2,1] => 00000
[5,1,2,3,4,6] => 00001
[5,1,2,3,6,4] => 00000
[5,1,2,4,3,6] => 00001
[5,1,2,4,6,3] => 00000
[5,1,2,6,3,4] => 00000
[5,1,2,6,4,3] => 00000
[5,1,3,2,4,6] => 00001
[5,1,3,2,6,4] => 00000
[5,1,3,4,2,6] => 00001
[5,1,3,4,6,2] => 00000
[5,1,3,6,2,4] => 00000
[5,1,3,6,4,2] => 00000
[5,1,4,2,3,6] => 00001
[5,1,4,2,6,3] => 00000
[5,1,4,3,2,6] => 00001
[5,1,4,3,6,2] => 00000
[5,1,4,6,2,3] => 00000
[5,1,4,6,3,2] => 00000
[5,1,6,2,3,4] => 00000
[5,1,6,2,4,3] => 00000
[5,1,6,3,2,4] => 00000
[5,1,6,3,4,2] => 00000
[5,1,6,4,2,3] => 00000
[5,1,6,4,3,2] => 00000
[5,2,1,3,4,6] => 00001
[5,2,1,3,6,4] => 00000
[5,2,1,4,3,6] => 00001
[5,2,1,4,6,3] => 00000
[5,2,1,6,3,4] => 00000
[5,2,1,6,4,3] => 00000
[5,2,3,1,4,6] => 00001
[5,2,3,1,6,4] => 00000
[5,2,3,4,1,6] => 00001
[5,2,3,4,6,1] => 00000
[5,2,3,6,1,4] => 00000
[5,2,3,6,4,1] => 00000
[5,2,4,1,3,6] => 00001
[5,2,4,1,6,3] => 00000
[5,2,4,3,1,6] => 00001
[5,2,4,3,6,1] => 00000
[5,2,4,6,1,3] => 00000
[5,2,4,6,3,1] => 00000
[5,2,6,1,3,4] => 00000
[5,2,6,1,4,3] => 00000
[5,2,6,3,1,4] => 00000
[5,2,6,3,4,1] => 00000
[5,2,6,4,1,3] => 00000
[5,2,6,4,3,1] => 00000
[5,3,1,2,4,6] => 00001
[5,3,1,2,6,4] => 00000
[5,3,1,4,2,6] => 00001
[5,3,1,4,6,2] => 00000
[5,3,1,6,2,4] => 00000
[5,3,1,6,4,2] => 00000
[5,3,2,1,4,6] => 00001
[5,3,2,1,6,4] => 00000
[5,3,2,4,1,6] => 00001
[5,3,2,4,6,1] => 00000
[5,3,2,6,1,4] => 00000
[5,3,2,6,4,1] => 00000
[5,3,4,1,2,6] => 00001
[5,3,4,1,6,2] => 00000
[5,3,4,2,1,6] => 00001
[5,3,4,2,6,1] => 00000
[5,3,4,6,1,2] => 00000
[5,3,4,6,2,1] => 00000
[5,3,6,1,2,4] => 00000
[5,3,6,1,4,2] => 00000
[5,3,6,2,1,4] => 00000
[5,3,6,2,4,1] => 00000
[5,3,6,4,1,2] => 00000
[5,3,6,4,2,1] => 00000
[5,4,1,2,3,6] => 00001
[5,4,1,2,6,3] => 00000
[5,4,1,3,2,6] => 00001
[5,4,1,3,6,2] => 00000
[5,4,1,6,2,3] => 00000
[5,4,1,6,3,2] => 00000
[5,4,2,1,3,6] => 00001
[5,4,2,1,6,3] => 00000
[5,4,2,3,1,6] => 00001
[5,4,2,3,6,1] => 00000
[5,4,2,6,1,3] => 00000
[5,4,2,6,3,1] => 00000
[5,4,3,1,2,6] => 00001
[5,4,3,1,6,2] => 00000
[5,4,3,2,1,6] => 00001
[5,4,3,2,6,1] => 00000
[5,4,3,6,1,2] => 00000
[5,4,3,6,2,1] => 00000
[5,4,6,1,2,3] => 00000
[5,4,6,1,3,2] => 00000
[5,4,6,2,1,3] => 00000
[5,4,6,2,3,1] => 00000
[5,4,6,3,1,2] => 00000
[5,4,6,3,2,1] => 00000
[5,6,1,2,3,4] => 00000
[5,6,1,2,4,3] => 00000
[5,6,1,3,2,4] => 00000
[5,6,1,3,4,2] => 00000
[5,6,1,4,2,3] => 00000
[5,6,1,4,3,2] => 00000
[5,6,2,1,3,4] => 00000
[5,6,2,1,4,3] => 00000
[5,6,2,3,1,4] => 00000
[5,6,2,3,4,1] => 00000
[5,6,2,4,1,3] => 00000
[5,6,2,4,3,1] => 00000
[5,6,3,1,2,4] => 00000
[5,6,3,1,4,2] => 00000
[5,6,3,2,1,4] => 00000
[5,6,3,2,4,1] => 00000
[5,6,3,4,1,2] => 00000
[5,6,3,4,2,1] => 00000
[5,6,4,1,2,3] => 00000
[5,6,4,1,3,2] => 00000
[5,6,4,2,1,3] => 00000
[5,6,4,2,3,1] => 00000
[5,6,4,3,1,2] => 00000
[5,6,4,3,2,1] => 00000
[6,1,2,3,4,5] => 00000
[6,1,2,3,5,4] => 00000
[6,1,2,4,3,5] => 00000
[6,1,2,4,5,3] => 00000
[6,1,2,5,3,4] => 00000
[6,1,2,5,4,3] => 00000
[6,1,3,2,4,5] => 00000
[6,1,3,2,5,4] => 00000
[6,1,3,4,2,5] => 00000
[6,1,3,4,5,2] => 00000
[6,1,3,5,2,4] => 00000
[6,1,3,5,4,2] => 00000
[6,1,4,2,3,5] => 00000
[6,1,4,2,5,3] => 00000
[6,1,4,3,2,5] => 00000
[6,1,4,3,5,2] => 00000
[6,1,4,5,2,3] => 00000
[6,1,4,5,3,2] => 00000
[6,1,5,2,3,4] => 00000
[6,1,5,2,4,3] => 00000
[6,1,5,3,2,4] => 00000
[6,1,5,3,4,2] => 00000
[6,1,5,4,2,3] => 00000
[6,1,5,4,3,2] => 00000
[6,2,1,3,4,5] => 00000
[6,2,1,3,5,4] => 00000
[6,2,1,4,3,5] => 00000
[6,2,1,4,5,3] => 00000
[6,2,1,5,3,4] => 00000
[6,2,1,5,4,3] => 00000
[6,2,3,1,4,5] => 00000
[6,2,3,1,5,4] => 00000
[6,2,3,4,1,5] => 00000
[6,2,3,4,5,1] => 00000
[6,2,3,5,1,4] => 00000
[6,2,3,5,4,1] => 00000
[6,2,4,1,3,5] => 00000
[6,2,4,1,5,3] => 00000
[6,2,4,3,1,5] => 00000
[6,2,4,3,5,1] => 00000
[6,2,4,5,1,3] => 00000
[6,2,4,5,3,1] => 00000
[6,2,5,1,3,4] => 00000
[6,2,5,1,4,3] => 00000
[6,2,5,3,1,4] => 00000
[6,2,5,3,4,1] => 00000
[6,2,5,4,1,3] => 00000
[6,2,5,4,3,1] => 00000
[6,3,1,2,4,5] => 00000
[6,3,1,2,5,4] => 00000
[6,3,1,4,2,5] => 00000
[6,3,1,4,5,2] => 00000
[6,3,1,5,2,4] => 00000
[6,3,1,5,4,2] => 00000
[6,3,2,1,4,5] => 00000
[6,3,2,1,5,4] => 00000
[6,3,2,4,1,5] => 00000
[6,3,2,4,5,1] => 00000
[6,3,2,5,1,4] => 00000
[6,3,2,5,4,1] => 00000
[6,3,4,1,2,5] => 00000
[6,3,4,1,5,2] => 00000
[6,3,4,2,1,5] => 00000
[6,3,4,2,5,1] => 00000
[6,3,4,5,1,2] => 00000
[6,3,4,5,2,1] => 00000
[6,3,5,1,2,4] => 00000
[6,3,5,1,4,2] => 00000
[6,3,5,2,1,4] => 00000
[6,3,5,2,4,1] => 00000
[6,3,5,4,1,2] => 00000
[6,3,5,4,2,1] => 00000
[6,4,1,2,3,5] => 00000
[6,4,1,2,5,3] => 00000
[6,4,1,3,2,5] => 00000
[6,4,1,3,5,2] => 00000
[6,4,1,5,2,3] => 00000
[6,4,1,5,3,2] => 00000
[6,4,2,1,3,5] => 00000
[6,4,2,1,5,3] => 00000
[6,4,2,3,1,5] => 00000
[6,4,2,3,5,1] => 00000
[6,4,2,5,1,3] => 00000
[6,4,2,5,3,1] => 00000
[6,4,3,1,2,5] => 00000
[6,4,3,1,5,2] => 00000
[6,4,3,2,1,5] => 00000
[6,4,3,2,5,1] => 00000
[6,4,3,5,1,2] => 00000
[6,4,3,5,2,1] => 00000
[6,4,5,1,2,3] => 00000
[6,4,5,1,3,2] => 00000
[6,4,5,2,1,3] => 00000
[6,4,5,2,3,1] => 00000
[6,4,5,3,1,2] => 00000
[6,4,5,3,2,1] => 00000
[6,5,1,2,3,4] => 00000
[6,5,1,2,4,3] => 00000
[6,5,1,3,2,4] => 00000
[6,5,1,3,4,2] => 00000
[6,5,1,4,2,3] => 00000
[6,5,1,4,3,2] => 00000
[6,5,2,1,3,4] => 00000
[6,5,2,1,4,3] => 00000
[6,5,2,3,1,4] => 00000
[6,5,2,3,4,1] => 00000
[6,5,2,4,1,3] => 00000
[6,5,2,4,3,1] => 00000
[6,5,3,1,2,4] => 00000
[6,5,3,1,4,2] => 00000
[6,5,3,2,1,4] => 00000
[6,5,3,2,4,1] => 00000
[6,5,3,4,1,2] => 00000
[6,5,3,4,2,1] => 00000
[6,5,4,1,2,3] => 00000
[6,5,4,1,3,2] => 00000
[6,5,4,2,1,3] => 00000
[6,5,4,2,3,1] => 00000
[6,5,4,3,1,2] => 00000
[6,5,4,3,2,1] => 00000
[1,2,3,4,5,6,7] => 111111
[1,2,3,4,5,7,6] => 111110
[1,2,3,4,6,5,7] => 111101
[1,2,3,4,6,7,5] => 111100
[1,2,3,4,7,5,6] => 111100
[1,2,3,4,7,6,5] => 111100
[1,2,3,5,4,6,7] => 111011
[1,2,3,5,4,7,6] => 111010
[1,2,3,5,6,4,7] => 111001
[1,2,3,5,6,7,4] => 111000
[1,2,3,5,7,4,6] => 111000
[1,2,3,5,7,6,4] => 111000
[1,2,3,6,4,5,7] => 111001
[1,2,3,6,4,7,5] => 111000
[1,2,3,6,5,4,7] => 111001
[1,2,3,6,5,7,4] => 111000
[1,2,3,6,7,4,5] => 111000
[1,2,3,6,7,5,4] => 111000
[1,2,3,7,4,5,6] => 111000
[1,2,3,7,4,6,5] => 111000
[1,2,3,7,5,4,6] => 111000
[1,2,3,7,5,6,4] => 111000
[1,2,3,7,6,4,5] => 111000
[1,2,3,7,6,5,4] => 111000
[1,2,4,3,5,6,7] => 110111
[1,2,4,3,5,7,6] => 110110
[1,2,4,3,6,5,7] => 110101
[1,2,4,3,6,7,5] => 110100
[1,2,4,3,7,5,6] => 110100
[1,2,4,3,7,6,5] => 110100
[1,2,4,5,3,6,7] => 110011
[1,2,4,5,3,7,6] => 110010
[1,2,4,5,6,3,7] => 110001
[1,2,4,5,6,7,3] => 110000
[1,2,4,5,7,3,6] => 110000
[1,2,4,5,7,6,3] => 110000
[1,2,4,6,3,5,7] => 110001
[1,2,4,6,3,7,5] => 110000
[1,2,4,6,5,3,7] => 110001
[1,2,4,6,5,7,3] => 110000
[1,2,4,6,7,3,5] => 110000
[1,2,4,6,7,5,3] => 110000
[1,2,4,7,3,5,6] => 110000
[1,2,4,7,3,6,5] => 110000
[1,2,4,7,5,3,6] => 110000
[1,2,4,7,5,6,3] => 110000
[1,2,4,7,6,3,5] => 110000
[1,2,4,7,6,5,3] => 110000
[1,2,5,3,4,6,7] => 110011
[1,2,5,3,4,7,6] => 110010
[1,2,5,3,6,4,7] => 110001
[1,2,5,3,6,7,4] => 110000
[1,2,5,3,7,4,6] => 110000
[1,2,5,3,7,6,4] => 110000
[1,2,5,4,3,6,7] => 110011
[1,2,5,4,3,7,6] => 110010
[1,2,5,4,6,3,7] => 110001
[1,2,5,4,6,7,3] => 110000
[1,2,5,4,7,3,6] => 110000
[1,2,5,4,7,6,3] => 110000
[1,2,5,6,3,4,7] => 110001
[1,2,5,6,3,7,4] => 110000
[1,2,5,6,4,3,7] => 110001
[1,2,5,6,4,7,3] => 110000
[1,2,5,6,7,3,4] => 110000
[1,2,5,6,7,4,3] => 110000
[1,2,5,7,3,4,6] => 110000
[1,2,5,7,3,6,4] => 110000
[1,2,5,7,4,3,6] => 110000
[1,2,5,7,4,6,3] => 110000
[1,2,5,7,6,3,4] => 110000
[1,2,5,7,6,4,3] => 110000
[1,2,6,3,4,5,7] => 110001
[1,2,6,3,4,7,5] => 110000
[1,2,6,3,5,4,7] => 110001
[1,2,6,3,5,7,4] => 110000
[1,2,6,3,7,4,5] => 110000
[1,2,6,3,7,5,4] => 110000
[1,2,6,4,3,5,7] => 110001
[1,2,6,4,3,7,5] => 110000
[1,2,6,4,5,3,7] => 110001
[1,2,6,4,5,7,3] => 110000
[1,2,6,4,7,3,5] => 110000
[1,2,6,4,7,5,3] => 110000
[1,2,6,5,3,4,7] => 110001
[1,2,6,5,3,7,4] => 110000
[1,2,6,5,4,3,7] => 110001
[1,2,6,5,4,7,3] => 110000
[1,2,6,5,7,3,4] => 110000
[1,2,6,5,7,4,3] => 110000
[1,2,6,7,3,4,5] => 110000
[1,2,6,7,3,5,4] => 110000
[1,2,6,7,4,3,5] => 110000
[1,2,6,7,4,5,3] => 110000
[1,2,6,7,5,3,4] => 110000
[1,2,6,7,5,4,3] => 110000
[1,2,7,3,4,5,6] => 110000
[1,2,7,3,4,6,5] => 110000
[1,2,7,3,5,4,6] => 110000
[1,2,7,3,5,6,4] => 110000
[1,2,7,3,6,4,5] => 110000
[1,2,7,3,6,5,4] => 110000
[1,2,7,4,3,5,6] => 110000
[1,2,7,4,3,6,5] => 110000
[1,2,7,4,5,3,6] => 110000
[1,2,7,4,5,6,3] => 110000
[1,2,7,4,6,3,5] => 110000
[1,2,7,4,6,5,3] => 110000
[1,2,7,5,3,4,6] => 110000
[1,2,7,5,3,6,4] => 110000
[1,2,7,5,4,3,6] => 110000
[1,2,7,5,4,6,3] => 110000
[1,2,7,5,6,3,4] => 110000
[1,2,7,5,6,4,3] => 110000
[1,2,7,6,3,4,5] => 110000
[1,2,7,6,3,5,4] => 110000
[1,2,7,6,4,3,5] => 110000
[1,2,7,6,4,5,3] => 110000
[1,2,7,6,5,3,4] => 110000
[1,2,7,6,5,4,3] => 110000
[1,3,2,4,5,6,7] => 101111
[1,3,2,4,5,7,6] => 101110
[1,3,2,4,6,5,7] => 101101
[1,3,2,4,6,7,5] => 101100
[1,3,2,4,7,5,6] => 101100
[1,3,2,4,7,6,5] => 101100
[1,3,2,5,4,6,7] => 101011
[1,3,2,5,4,7,6] => 101010
[1,3,2,5,6,4,7] => 101001
[1,3,2,5,6,7,4] => 101000
[1,3,2,5,7,4,6] => 101000
[1,3,2,5,7,6,4] => 101000
[1,3,2,6,4,5,7] => 101001
[1,3,2,6,4,7,5] => 101000
[1,3,2,6,5,4,7] => 101001
[1,3,2,6,5,7,4] => 101000
[1,3,2,6,7,4,5] => 101000
[1,3,2,6,7,5,4] => 101000
[1,3,2,7,4,5,6] => 101000
[1,3,2,7,4,6,5] => 101000
[1,3,2,7,5,4,6] => 101000
[1,3,2,7,5,6,4] => 101000
[1,3,2,7,6,4,5] => 101000
[1,3,2,7,6,5,4] => 101000
[1,3,4,2,5,6,7] => 100111
[1,3,4,2,5,7,6] => 100110
[1,3,4,2,6,5,7] => 100101
[1,3,4,2,6,7,5] => 100100
[1,3,4,2,7,5,6] => 100100
[1,3,4,2,7,6,5] => 100100
[1,3,4,5,2,6,7] => 100011
[1,3,4,5,2,7,6] => 100010
[1,3,4,5,6,2,7] => 100001
[1,3,4,5,6,7,2] => 100000
[1,3,4,5,7,2,6] => 100000
[1,3,4,5,7,6,2] => 100000
[1,3,4,6,2,5,7] => 100001
[1,3,4,6,2,7,5] => 100000
[1,3,4,6,5,2,7] => 100001
[1,3,4,6,5,7,2] => 100000
[1,3,4,6,7,2,5] => 100000
[1,3,4,6,7,5,2] => 100000
[1,3,4,7,2,5,6] => 100000
[1,3,4,7,2,6,5] => 100000
[1,3,4,7,5,2,6] => 100000
[1,3,4,7,5,6,2] => 100000
[1,3,4,7,6,2,5] => 100000
[1,3,4,7,6,5,2] => 100000
[1,3,5,2,4,6,7] => 100011
[1,3,5,2,4,7,6] => 100010
[1,3,5,2,6,4,7] => 100001
[1,3,5,2,6,7,4] => 100000
[1,3,5,2,7,4,6] => 100000
[1,3,5,2,7,6,4] => 100000
[1,3,5,4,2,6,7] => 100011
[1,3,5,4,2,7,6] => 100010
[1,3,5,4,6,2,7] => 100001
[1,3,5,4,6,7,2] => 100000
[1,3,5,4,7,2,6] => 100000
[1,3,5,4,7,6,2] => 100000
[1,3,5,6,2,4,7] => 100001
[1,3,5,6,2,7,4] => 100000
[1,3,5,6,4,2,7] => 100001
[1,3,5,6,4,7,2] => 100000
[1,3,5,6,7,2,4] => 100000
[1,3,5,6,7,4,2] => 100000
[1,3,5,7,2,4,6] => 100000
[1,3,5,7,2,6,4] => 100000
[1,3,5,7,4,2,6] => 100000
[1,3,5,7,4,6,2] => 100000
[1,3,5,7,6,2,4] => 100000
[1,3,5,7,6,4,2] => 100000
[1,3,6,2,4,5,7] => 100001
[1,3,6,2,4,7,5] => 100000
[1,3,6,2,5,4,7] => 100001
[1,3,6,2,5,7,4] => 100000
[1,3,6,2,7,4,5] => 100000
[1,3,6,2,7,5,4] => 100000
[1,3,6,4,2,5,7] => 100001
[1,3,6,4,2,7,5] => 100000
[1,3,6,4,5,2,7] => 100001
[1,3,6,4,5,7,2] => 100000
[1,3,6,4,7,2,5] => 100000
[1,3,6,4,7,5,2] => 100000
[1,3,6,5,2,4,7] => 100001
[1,3,6,5,2,7,4] => 100000
[1,3,6,5,4,2,7] => 100001
[1,3,6,5,4,7,2] => 100000
[1,3,6,5,7,2,4] => 100000
[1,3,6,5,7,4,2] => 100000
[1,3,6,7,2,4,5] => 100000
[1,3,6,7,2,5,4] => 100000
[1,3,6,7,4,2,5] => 100000
[1,3,6,7,4,5,2] => 100000
[1,3,6,7,5,2,4] => 100000
[1,3,6,7,5,4,2] => 100000
[1,3,7,2,4,5,6] => 100000
[1,3,7,2,4,6,5] => 100000
[1,3,7,2,5,4,6] => 100000
[1,3,7,2,5,6,4] => 100000
[1,3,7,2,6,4,5] => 100000
[1,3,7,2,6,5,4] => 100000
[1,3,7,4,2,5,6] => 100000
[1,3,7,4,2,6,5] => 100000
[1,3,7,4,5,2,6] => 100000
[1,3,7,4,5,6,2] => 100000
[1,3,7,4,6,2,5] => 100000
[1,3,7,4,6,5,2] => 100000
[1,3,7,5,2,4,6] => 100000
[1,3,7,5,2,6,4] => 100000
[1,3,7,5,4,2,6] => 100000
[1,3,7,5,4,6,2] => 100000
[1,3,7,5,6,2,4] => 100000
[1,3,7,5,6,4,2] => 100000
[1,3,7,6,2,4,5] => 100000
[1,3,7,6,2,5,4] => 100000
[1,3,7,6,4,2,5] => 100000
[1,3,7,6,4,5,2] => 100000
[1,3,7,6,5,2,4] => 100000
[1,3,7,6,5,4,2] => 100000
[1,4,2,3,5,6,7] => 100111
[1,4,2,3,5,7,6] => 100110
[1,4,2,3,6,5,7] => 100101
[1,4,2,3,6,7,5] => 100100
[1,4,2,3,7,5,6] => 100100
[1,4,2,3,7,6,5] => 100100
[1,4,2,5,3,6,7] => 100011
[1,4,2,5,3,7,6] => 100010
[1,4,2,5,6,3,7] => 100001
[1,4,2,5,6,7,3] => 100000
[1,4,2,5,7,3,6] => 100000
[1,4,2,5,7,6,3] => 100000
[1,4,2,6,3,5,7] => 100001
[1,4,2,6,3,7,5] => 100000
[1,4,2,6,5,3,7] => 100001
[1,4,2,6,5,7,3] => 100000
[1,4,2,6,7,3,5] => 100000
[1,4,2,6,7,5,3] => 100000
[1,4,2,7,3,5,6] => 100000
[1,4,2,7,3,6,5] => 100000
[1,4,2,7,5,3,6] => 100000
[1,4,2,7,5,6,3] => 100000
[1,4,2,7,6,3,5] => 100000
[1,4,2,7,6,5,3] => 100000
[1,4,3,2,5,6,7] => 100111
[1,4,3,2,5,7,6] => 100110
[1,4,3,2,6,5,7] => 100101
[1,4,3,2,6,7,5] => 100100
[1,4,3,2,7,5,6] => 100100
[1,4,3,2,7,6,5] => 100100
[1,4,3,5,2,6,7] => 100011
[1,4,3,5,2,7,6] => 100010
[1,4,3,5,6,2,7] => 100001
[1,4,3,5,6,7,2] => 100000
[1,4,3,5,7,2,6] => 100000
[1,4,3,5,7,6,2] => 100000
[1,4,3,6,2,5,7] => 100001
[1,4,3,6,2,7,5] => 100000
[1,4,3,6,5,2,7] => 100001
[1,4,3,6,5,7,2] => 100000
[1,4,3,6,7,2,5] => 100000
[1,4,3,6,7,5,2] => 100000
[1,4,3,7,2,5,6] => 100000
[1,4,3,7,2,6,5] => 100000
[1,4,3,7,5,2,6] => 100000
[1,4,3,7,5,6,2] => 100000
[1,4,3,7,6,2,5] => 100000
[1,4,3,7,6,5,2] => 100000
[1,4,5,2,3,6,7] => 100011
[1,4,5,2,3,7,6] => 100010
[1,4,5,2,6,3,7] => 100001
[1,4,5,2,6,7,3] => 100000
[1,4,5,2,7,3,6] => 100000
[1,4,5,2,7,6,3] => 100000
[1,4,5,3,2,6,7] => 100011
[1,4,5,3,2,7,6] => 100010
[1,4,5,3,6,2,7] => 100001
[1,4,5,3,6,7,2] => 100000
[1,4,5,3,7,2,6] => 100000
[1,4,5,3,7,6,2] => 100000
[1,4,5,6,2,3,7] => 100001
[1,4,5,6,2,7,3] => 100000
[1,4,5,6,3,2,7] => 100001
[1,4,5,6,3,7,2] => 100000
[1,4,5,6,7,2,3] => 100000
[1,4,5,6,7,3,2] => 100000
[1,4,5,7,2,3,6] => 100000
[1,4,5,7,2,6,3] => 100000
[1,4,5,7,3,2,6] => 100000
[1,4,5,7,3,6,2] => 100000
[1,4,5,7,6,2,3] => 100000
[1,4,5,7,6,3,2] => 100000
[1,4,6,2,3,5,7] => 100001
[1,4,6,2,3,7,5] => 100000
[1,4,6,2,5,3,7] => 100001
[1,4,6,2,5,7,3] => 100000
[1,4,6,2,7,3,5] => 100000
[1,4,6,2,7,5,3] => 100000
[1,4,6,3,2,5,7] => 100001
[1,4,6,3,2,7,5] => 100000
[1,4,6,3,5,2,7] => 100001
[1,4,6,3,5,7,2] => 100000
[1,4,6,3,7,2,5] => 100000
[1,4,6,3,7,5,2] => 100000
[1,4,6,5,2,3,7] => 100001
[1,4,6,5,2,7,3] => 100000
[1,4,6,5,3,2,7] => 100001
Download as text // json // pdf
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
$$C(\pi)=\{i\in [n-1] : \forall 1 \leq j \leq i < k \leq n \quad \pi(j)<\pi(k)\}.$$
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.
Properties
surjectiveA map $\phi: A \rightarrow B$ is surjective if for any $b \in B$, there is an $a \in A$ such that $\phi(a) = b$., gradedA map $\phi: A \rightarrow B$ is graded for graded sets $A$ and $B$ if $\operatorname{deg}(a) = \operatorname{deg}(a')$ implies $\operatorname{deg}(\phi(a)) = \operatorname{deg}(\phi(a'))$ for all $a, a' \in A$.
References
[1] Stanley, R. P. The Descent Set and Connectivity Set of a Permutation arXiv:math/0507224 MathSciNet:2167418
[2] Bergeron, N., Hohlweg, C., Zabrocki, M. Posets related to the connectivity set of Coxeter groups arXiv:math/0509271 MathSciNet:2255139
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
Code
def connectivity_set(pi):
    C = [1 if all(pi[j] < pi[k] for j in range(i) for k in range(i, len(pi))) else 0 for i in range(1, len(pi))]
    return Words([0,1])(C)