Identifier
Values
([],1) => [2] => 100 => 010 => 2
([],2) => [2,2] => 1100 => 1010 => 4
([(0,1)],2) => [3] => 1000 => 0010 => 3
([],3) => [2,2,2,2] => 111100 => 111010 => 8
([(1,2)],3) => [6] => 1000000 => 0000010 => 6
([(0,1),(0,2)],3) => [3,2] => 10100 => 10010 => 5
([(0,2),(2,1)],3) => [4] => 10000 => 00010 => 4
([(0,2),(1,2)],3) => [3,2] => 10100 => 10010 => 5
([(2,3)],4) => [6,6] => 11000000 => 00001010 => 12
([(1,2),(1,3)],4) => [6,2,2] => 100001100 => 110000010 => 10
([(0,1),(0,2),(0,3)],4) => [3,2,2,2] => 1011100 => 1110010 => 9
([(0,2),(0,3),(3,1)],4) => [7] => 10000000 => 00000010 => 7
([(0,1),(0,2),(1,3),(2,3)],4) => [4,2] => 100100 => 100010 => 6
([(1,2),(2,3)],4) => [4,4] => 110000 => 001010 => 8
([(0,3),(3,1),(3,2)],4) => [4,2] => 100100 => 100010 => 6
([(1,3),(2,3)],4) => [6,2,2] => 100001100 => 110000010 => 10
([(0,3),(1,3),(3,2)],4) => [4,2] => 100100 => 100010 => 6
([(0,3),(1,3),(2,3)],4) => [3,2,2,2] => 1011100 => 1110010 => 9
([(0,3),(1,2)],4) => [3,3,3] => 111000 => 101010 => 9
([(0,3),(1,2),(1,3)],4) => [5,3] => 1001000 => 0100010 => 8
([(0,2),(0,3),(1,2),(1,3)],4) => [3,2,2] => 101100 => 110010 => 7
([(0,3),(2,1),(3,2)],4) => [5] => 100000 => 000010 => 5
([(0,3),(1,2),(2,3)],4) => [7] => 10000000 => 00000010 => 7
([(0,2),(0,3),(0,4),(4,1)],5) => [7,6] => 101000000 => 000010010 => 13
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [4,2,2,2] => 10011100 => 11100010 => 10
([(1,2),(1,3),(2,4),(3,4)],5) => [4,4,2,2] => 11001100 => 00111010 => 12
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [5,2] => 1000100 => 1000010 => 7
([(0,3),(0,4),(3,2),(4,1)],5) => [4,3,3] => 1011000 => 1010010 => 10
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [5,4] => 1010000 => 0010010 => 9
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [4,2,2] => 1001100 => 1100010 => 8
([(2,3),(3,4)],5) => [4,4,4,4] => 11110000 => 10101010 => 16
([(1,4),(4,2),(4,3)],5) => [4,4,2,2] => 11001100 => 00111010 => 12
([(0,4),(4,1),(4,2),(4,3)],5) => [4,2,2,2] => 10011100 => 11100010 => 10
([(1,4),(2,4),(4,3)],5) => [4,4,2,2] => 11001100 => 00111010 => 12
([(0,4),(1,4),(4,2),(4,3)],5) => [4,2,2] => 1001100 => 1100010 => 8
([(0,4),(1,4),(2,4),(4,3)],5) => [4,2,2,2] => 10011100 => 11100010 => 10
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [5,3,2,2] => 100101100 => 011100010 => 12
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [3,2,2,2,2] => 10111100 => 11110010 => 11
([(0,4),(1,4),(2,3),(4,2)],5) => [5,2] => 1000100 => 1000010 => 7
([(0,4),(1,4),(2,3),(2,4)],5) => [6,5,3] => 101001000 => 100010010 => 14
([(0,4),(1,4),(2,3),(3,4)],5) => [7,6] => 101000000 => 000010010 => 13
([(1,4),(2,3)],5) => [6,6,6] => 111000000 => 000101010 => 18
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [5,4] => 1010000 => 0010010 => 9
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [7,2] => 100000100 => 100000010 => 9
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [4,2,2] => 1001100 => 1100010 => 8
([(0,4),(1,2),(1,4),(4,3)],5) => [10] => 10000000000 => 00000000010 => 10
([(0,4),(1,2),(1,3),(1,4)],5) => [6,5,3] => 101001000 => 100010010 => 14
([(0,2),(0,4),(3,1),(4,3)],5) => [5,4] => 1010000 => 0010010 => 9
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [8] => 100000000 => 000000010 => 8
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [5,3,2,2] => 100101100 => 011100010 => 12
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [3,2,2,2,2] => 10111100 => 11110010 => 11
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [10] => 10000000000 => 00000000010 => 10
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [7,2] => 100000100 => 100000010 => 9
([(1,4),(3,2),(4,3)],5) => [10] => 10000000000 => 00000000010 => 10
([(0,3),(3,4),(4,1),(4,2)],5) => [5,2] => 1000100 => 1000010 => 7
([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 100000000 => 000000010 => 8
([(0,4),(3,2),(4,1),(4,3)],5) => [8] => 100000000 => 000000010 => 8
([(0,4),(1,2),(2,3),(2,4)],5) => [10] => 10000000000 => 00000000010 => 10
([(0,4),(2,3),(3,1),(4,2)],5) => [6] => 1000000 => 0000010 => 6
([(0,3),(1,2),(2,4),(3,4)],5) => [4,3,3] => 1011000 => 1010010 => 10
([(0,4),(1,2),(2,3),(3,4)],5) => [5,4] => 1010000 => 0010010 => 9
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [5,2] => 1000100 => 1000010 => 7
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [5,2,2,2] => 100011100 => 111000010 => 11
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [4,2,2,2,2] => 100111100 => 111100010 => 12
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => [6,5,4] => 101010000 => 010010010 => 15
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [5,2,2] => 10001100 => 11000010 => 9
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [8,2] => 1000000100 => 1000000010 => 10
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [5,2,2] => 10001100 => 11000010 => 9
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => [6,5,4] => 101010000 => 010010010 => 15
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [4,2,2,2,2] => 100111100 => 111100010 => 12
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [5,2,2,2] => 100011100 => 111000010 => 11
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => [4,2,2,2,2] => 100111100 => 111100010 => 12
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => [4,2,2,2,2] => 100111100 => 111100010 => 12
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [5,2,2,2] => 100011100 => 111000010 => 11
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [4,2,2,2,2] => 100111100 => 111100010 => 12
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [8,2] => 1000000100 => 1000000010 => 10
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => [6,5,4] => 101010000 => 010010010 => 15
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [5,2,2] => 10001100 => 11000010 => 9
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [5,3,3] => 10011000 => 10100010 => 11
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 10000100 => 10000010 => 8
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5,4,4,4] => 101110000 => 101010010 => 17
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [5,2,2,2] => 100011100 => 111000010 => 11
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,2,2] => 10001100 => 11000010 => 9
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => [6,4,3] => 100101000 => 100100010 => 13
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => [5,4,2] => 10100100 => 00110010 => 11
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [5,5] => 1100000 => 0001010 => 10
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => [4,3,3,2] => 10110100 => 10110010 => 12
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => [5,4,2] => 10100100 => 00110010 => 11
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [4,2,2,2] => 10011100 => 11100010 => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => [5,4,2] => 10100100 => 00110010 => 11
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [5,2,2] => 10001100 => 11000010 => 9
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => [8,2] => 1000000100 => 1000000010 => 10
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [6,5,4] => 101010000 => 010010010 => 15
([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => [5,4,4,4] => 101110000 => 101010010 => 17
>>> Load all 236 entries. <<<
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [5,5] => 1100000 => 0001010 => 10
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [9] => 1000000000 => 0000000010 => 9
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [6,4] => 10010000 => 00100010 => 10
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [6,2] => 10000100 => 10000010 => 8
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [4,2,2,2,2] => 100111100 => 111100010 => 12
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [5,4,2,2] => 101001100 => 001110010 => 13
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => [6,4,3] => 100101000 => 100100010 => 13
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => [7,5] => 100100000 => 000100010 => 12
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => [8,2] => 1000000100 => 1000000010 => 10
([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => [5,5,3] => 11001000 => 10001010 => 13
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [8,2] => 1000000100 => 1000000010 => 10
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => [6,4,3] => 100101000 => 100100010 => 13
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => [7,5] => 100100000 => 000100010 => 12
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => [8,2] => 1000000100 => 1000000010 => 10
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => [6,6] => 11000000 => 00001010 => 12
([(1,5),(3,4),(4,2),(5,3)],6) => [6,6] => 11000000 => 00001010 => 12
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [6,2] => 10000100 => 10000010 => 8
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [5,3,3] => 10011000 => 10100010 => 11
([(0,5),(1,4),(4,2),(5,3)],6) => [4,4,4,4] => 11110000 => 10101010 => 16
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => [6,4] => 10010000 => 00100010 => 10
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => [4,3,3,2] => 10110100 => 10110010 => 12
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [6,2] => 10000100 => 10000010 => 8
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [6,4] => 10010000 => 00100010 => 10
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => [7,5] => 100100000 => 000100010 => 12
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => [5,4,2] => 10100100 => 00110010 => 11
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [5,2,2] => 10001100 => 11000010 => 9
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => [5,5] => 1100000 => 0001010 => 10
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => [5,3,3] => 10011000 => 10100010 => 11
([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => [5,5,3] => 11001000 => 10001010 => 13
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [9] => 1000000000 => 0000000010 => 9
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => [7,5] => 100100000 => 000100010 => 12
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [7] => 10000000 => 00000010 => 7
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1000000000 => 0000000010 => 9
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [6,2] => 10000100 => 10000010 => 8
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [9] => 1000000000 => 0000000010 => 9
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => [5,5,2,2] => 110001100 => 000111010 => 14
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => [5,3,3,2] => 100110100 => 101100010 => 13
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => [5,5,2] => 11000100 => 00011010 => 12
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [5,2,2,2] => 100011100 => 111000010 => 11
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => [5,5,2,2] => 110001100 => 000111010 => 14
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => [6,5,5] => 101100000 => 001010010 => 16
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => [6,5,5] => 101100000 => 001010010 => 16
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => [6,4,2] => 100100100 => 001100010 => 12
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [7,2] => 100000100 => 100000010 => 9
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [7,2] => 100000100 => 100000010 => 9
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => [5,3,3,2] => 100110100 => 101100010 => 13
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => [5,5,2] => 11000100 => 00011010 => 12
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => [5,2,2,2] => 100011100 => 111000010 => 11
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => [5,3,3,2] => 100110100 => 101100010 => 13
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => [5,5,2] => 11000100 => 00011010 => 12
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [5,2,2,2] => 100011100 => 111000010 => 11
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => [5,5,2] => 11000100 => 00011010 => 12
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => [5,2,2,2] => 100011100 => 111000010 => 11
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => [5,3,3,2] => 100110100 => 101100010 => 13
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => [6,4,2] => 100100100 => 001100010 => 12
([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => [5,5,4,2] => 110100100 => 010011010 => 16
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [5,5,2,2] => 110001100 => 000111010 => 14
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => [6,5,5] => 101100000 => 001010010 => 16
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => [6,5,5] => 101100000 => 001010010 => 16
([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => [5,5,2] => 11000100 => 00011010 => 12
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [6,5] => 10100000 => 00010010 => 11
([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => [7,4] => 100010000 => 001000010 => 11
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) => [6,4,2] => 100100100 => 001100010 => 12
([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [7,2] => 100000100 => 100000010 => 9
([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => [5,5,2,2] => 110001100 => 000111010 => 14
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) => [6,4,2] => 100100100 => 001100010 => 12
([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => [6,3,3] => 100011000 => 101000010 => 12
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7) => [5,5,2,2] => 110001100 => 000111010 => 14
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,6),(4,6),(5,3),(5,6)],7) => [5,5,4,2] => 110100100 => 010011010 => 16
([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [6,5] => 10100000 => 00010010 => 11
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [6,4,2] => 100100100 => 001100010 => 12
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7) => [5,3,3,2] => 100110100 => 101100010 => 13
([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [5,3,3,2] => 100110100 => 101100010 => 13
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [10] => 10000000000 => 00000000010 => 10
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7) => [6,4,2] => 100100100 => 001100010 => 12
([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => [5,5,2] => 11000100 => 00011010 => 12
([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => [6,5] => 10100000 => 00010010 => 11
([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3),(5,4)],7) => [6,5,5] => 101100000 => 001010010 => 16
([(0,5),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4)],7) => [6,5,5] => 101100000 => 001010010 => 16
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => [5,4,4,4] => 101110000 => 101010010 => 17
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [10] => 10000000000 => 00000000010 => 10
([(0,4),(2,5),(2,6),(3,1),(3,5),(3,6),(4,2),(4,3)],7) => [5,5,2,2] => 110001100 => 000111010 => 14
([(0,5),(0,6),(1,3),(1,5),(1,6),(3,4),(4,2),(6,4)],7) => [5,5,4,2] => 110100100 => 010011010 => 16
([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7) => [6,5,5] => 101100000 => 001010010 => 16
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [6,2,2] => 100001100 => 110000010 => 10
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => [6,5] => 10100000 => 00010010 => 11
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [7,2] => 100000100 => 100000010 => 9
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => [7,4] => 100010000 => 001000010 => 11
([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => [6,6,6] => 111000000 => 000101010 => 18
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => [6,3,3] => 100011000 => 101000010 => 12
([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [10] => 10000000000 => 00000000010 => 10
([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7) => [6,5,3] => 101001000 => 100010010 => 14
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 100000000 => 000000010 => 8
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 10000000000 => 00000000010 => 10
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [10] => 10000000000 => 00000000010 => 10
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => [6,3,3] => 100011000 => 101000010 => 12
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [6,3,3] => 100011000 => 101000010 => 12
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [7,2] => 100000100 => 100000010 => 9
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [7,4] => 100010000 => 001000010 => 11
([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [7,6] => 101000000 => 000010010 => 13
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [7,2] => 100000100 => 100000010 => 9
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [5,4,4,4] => 101110000 => 101010010 => 17
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => [7,4] => 100010000 => 001000010 => 11
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [7,5] => 100100000 => 000100010 => 12
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Description
The major index of a binary word.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.