- FindStat

Identifier

Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
St000326: Binary words ⟶ ℤ

Values

([],1) => [2] => 100 => 001 => 3

([],2) => [2,2] => 1100 => 0011 => 3

([(0,1)],2) => [3] => 1000 => 0001 => 4

([],3) => [2,2,2,2] => 111100 => 001111 => 3

([(1,2)],3) => [6] => 1000000 => 0000001 => 7

([(0,1),(0,2)],3) => [3,2] => 10100 => 00101 => 3

([(0,2),(2,1)],3) => [4] => 10000 => 00001 => 5

([(0,2),(1,2)],3) => [3,2] => 10100 => 00101 => 3

([(2,3)],4) => [6,6] => 11000000 => 00000011 => 7

([(1,2),(1,3)],4) => [6,2,2] => 100001100 => 001100001 => 3

([(0,1),(0,2),(0,3)],4) => [3,2,2,2] => 1011100 => 0011101 => 3

([(0,2),(0,3),(3,1)],4) => [7] => 10000000 => 00000001 => 8

([(0,1),(0,2),(1,3),(2,3)],4) => [4,2] => 100100 => 001001 => 3

([(1,2),(2,3)],4) => [4,4] => 110000 => 000011 => 5

([(0,3),(3,1),(3,2)],4) => [4,2] => 100100 => 001001 => 3

([(1,3),(2,3)],4) => [6,2,2] => 100001100 => 001100001 => 3

([(0,3),(1,3),(3,2)],4) => [4,2] => 100100 => 001001 => 3

([(0,3),(1,3),(2,3)],4) => [3,2,2,2] => 1011100 => 0011101 => 3

([(0,3),(1,2)],4) => [3,3,3] => 111000 => 000111 => 4

([(0,3),(1,2),(1,3)],4) => [5,3] => 1001000 => 0001001 => 4

([(0,2),(0,3),(1,2),(1,3)],4) => [3,2,2] => 101100 => 001101 => 3

([(0,3),(2,1),(3,2)],4) => [5] => 100000 => 000001 => 6

([(0,3),(1,2),(2,3)],4) => [7] => 10000000 => 00000001 => 8

([(3,4)],5) => [6,6,6,6] => 1111000000 => 0000001111 => 7

([(0,1),(0,2),(0,3),(0,4)],5) => [3,2,2,2,2,2,2,2] => 10111111100 => 00111111101 => 3

([(0,2),(0,3),(0,4),(4,1)],5) => [7,6] => 101000000 => 000000101 => 7

([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [4,2,2,2] => 10011100 => 00111001 => 3

([(1,2),(1,3),(2,4),(3,4)],5) => [4,4,2,2] => 11001100 => 00110011 => 3

([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [5,2] => 1000100 => 0010001 => 3

([(0,3),(0,4),(3,2),(4,1)],5) => [4,3,3] => 1011000 => 0001101 => 4

([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [5,4] => 1010000 => 0000101 => 5

([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [4,2,2] => 1001100 => 0011001 => 3

([(2,3),(3,4)],5) => [4,4,4,4] => 11110000 => 00001111 => 5

([(1,4),(4,2),(4,3)],5) => [4,4,2,2] => 11001100 => 00110011 => 3

([(0,4),(4,1),(4,2),(4,3)],5) => [4,2,2,2] => 10011100 => 00111001 => 3

([(1,4),(2,4),(4,3)],5) => [4,4,2,2] => 11001100 => 00110011 => 3

([(0,4),(1,4),(4,2),(4,3)],5) => [4,2,2] => 1001100 => 0011001 => 3

([(0,4),(1,4),(2,4),(4,3)],5) => [4,2,2,2] => 10011100 => 00111001 => 3

([(0,4),(1,4),(2,4),(3,4)],5) => [3,2,2,2,2,2,2,2] => 10111111100 => 00111111101 => 3

([(0,4),(1,4),(2,3)],5) => [6,3,3,3] => 1000111000 => 0001110001 => 4

([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [5,3,2,2] => 100101100 => 001101001 => 3

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [3,2,2,2,2] => 10111100 => 00111101 => 3

([(0,4),(1,4),(2,3),(4,2)],5) => [5,2] => 1000100 => 0010001 => 3

([(0,4),(1,4),(2,3),(2,4)],5) => [6,5,3] => 101001000 => 000100101 => 4

([(0,4),(1,4),(2,3),(3,4)],5) => [7,6] => 101000000 => 000000101 => 7

([(1,4),(2,3)],5) => [6,6,6] => 111000000 => 000000111 => 7

([(0,4),(1,2),(1,4),(2,3)],5) => [8,3] => 1000001000 => 0001000001 => 4

([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [5,4] => 1010000 => 0000101 => 5

([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [7,2] => 100000100 => 001000001 => 3

([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [4,2,2] => 1001100 => 0011001 => 3

([(0,4),(1,2),(1,4),(4,3)],5) => [10] => 10000000000 => 00000000001 => 11

([(0,4),(1,2),(1,3)],5) => [6,3,3,3] => 1000111000 => 0001110001 => 4

([(0,4),(1,2),(1,3),(1,4)],5) => [6,5,3] => 101001000 => 000100101 => 4

([(0,2),(0,4),(3,1),(4,3)],5) => [5,4] => 1010000 => 0000101 => 5

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [8] => 100000000 => 000000001 => 9

([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [5,3,2,2] => 100101100 => 001101001 => 3

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [3,2,2,2,2] => 10111100 => 00111101 => 3

([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [10] => 10000000000 => 00000000001 => 11

([(0,3),(1,2),(1,4),(3,4)],5) => [8,3] => 1000001000 => 0001000001 => 4

([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [7,2] => 100000100 => 001000001 => 3

([(1,4),(3,2),(4,3)],5) => [10] => 10000000000 => 00000000001 => 11

([(0,3),(3,4),(4,1),(4,2)],5) => [5,2] => 1000100 => 0010001 => 3

([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 100000000 => 000000001 => 9

([(0,4),(3,2),(4,1),(4,3)],5) => [8] => 100000000 => 000000001 => 9

([(0,4),(1,2),(2,3),(2,4)],5) => [10] => 10000000000 => 00000000001 => 11

([(0,4),(2,3),(3,1),(4,2)],5) => [6] => 1000000 => 0000001 => 7

([(0,3),(1,2),(2,4),(3,4)],5) => [4,3,3] => 1011000 => 0001101 => 4

([(0,4),(1,2),(2,3),(3,4)],5) => [5,4] => 1010000 => 0000101 => 5

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [5,2] => 1000100 => 0010001 => 3

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [5,2,2,2] => 100011100 => 001110001 => 3

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => [6,4,3,3] => 1001011000 => 0001101001 => 4

([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => [8,4,2] => 10000100100 => 00100100001 => 3

([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(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 => 001111001 => 3

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => [6,5,4] => 101010000 => 000010101 => 5

([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => [7,6,6] => 1011000000 => 0000001101 => 7

([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [5,2,2] => 10001100 => 00110001 => 3

([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [8,2] => 1000000100 => 0010000001 => 3

([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [5,2,2] => 10001100 => 00110001 => 3

([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => [6,4,3,3] => 1001011000 => 0001101001 => 4

([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => [6,5,4] => 101010000 => 000010101 => 5

([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => [8,4,2] => 10000100100 => 00100100001 => 3

([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [4,2,2,2,2] => 100111100 => 001111001 => 3

([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [5,2,2,2] => 100011100 => 001110001 => 3

([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => [4,2,2,2,2] => 100111100 => 001111001 => 3

([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => [4,2,2,2,2] => 100111100 => 001111001 => 3

([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [5,2,2,2] => 100011100 => 001110001 => 3

([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => [8,4,2] => 10000100100 => 00100100001 => 3

([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [4,2,2,2,2] => 100111100 => 001111001 => 3

([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [8,2] => 1000000100 => 0010000001 => 3

([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => [6,5,4] => 101010000 => 000010101 => 5

([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [5,2,2] => 10001100 => 00110001 => 3

([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => [8,6,3] => 10010001000 => 00010001001 => 4

([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [5,3,3] => 10011000 => 00011001 => 4

([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [8,6] => 1001000000 => 0000001001 => 7

([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 10000100 => 00100001 => 3

>>> Load all 359 entries. <<<

([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => [6,4,3,3] => 1001011000 => 0001101001 => 4

([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => [8,4,2] => 10000100100 => 00100100001 => 3

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5,4,4,4] => 101110000 => 000011101 => 5

([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [5,2,2,2] => 100011100 => 001110001 => 3

([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,2,2] => 10001100 => 00110001 => 3

([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => [8,6,3] => 10010001000 => 00010001001 => 4

([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => [6,4,3] => 100101000 => 000101001 => 4

([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => [5,4,2] => 10100100 => 00100101 => 3

([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [5,5] => 1100000 => 0000011 => 6

([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => [8,4] => 1000010000 => 0000100001 => 5

([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => [4,3,3,2] => 10110100 => 00101101 => 3

([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => [5,4,2] => 10100100 => 00100101 => 3

([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [4,2,2,2] => 10011100 => 00111001 => 3

([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => [5,4,2] => 10100100 => 00100101 => 3

([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [5,2,2] => 10001100 => 00110001 => 3

([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => [8,2] => 1000000100 => 0010000001 => 3

([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => [8,6,3] => 10010001000 => 00010001001 => 4

([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => [7,6,2] => 1010000100 => 0010000101 => 3

([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => [8,6,3] => 10010001000 => 00010001001 => 4

([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [6,5,4] => 101010000 => 000010101 => 5

([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => [5,4,4,4] => 101110000 => 000011101 => 5

([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => [8,6] => 1001000000 => 0000001001 => 7

([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [5,5] => 1100000 => 0000011 => 6

([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => [8,4,2] => 10000100100 => 00100100001 => 3

([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => [8,8] => 1100000000 => 0000000011 => 9

([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [9] => 1000000000 => 0000000001 => 10

([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [6,4] => 10010000 => 00001001 => 5

([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [6,4,3,3] => 1001011000 => 0001101001 => 4

([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [6,2] => 10000100 => 00100001 => 3

([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => [7,6,2] => 1010000100 => 0010000101 => 3

([(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 => 001111001 => 3

([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => [8,6,3] => 10010001000 => 00010001001 => 4

([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => [7,5,2] => 1001000100 => 0010001001 => 3

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [5,4,2,2] => 101001100 => 001100101 => 3

([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => [7,5,5] => 1001100000 => 0000011001 => 6

([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => [6,4,3] => 100101000 => 000101001 => 4

([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => [7,5] => 100100000 => 000001001 => 6

([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => [8,4] => 1000010000 => 0000100001 => 5

([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => [8,7] => 1010000000 => 0000000101 => 8

([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => [8,4,2] => 10000100100 => 00100100001 => 3

([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => [8,2] => 1000000100 => 0010000001 => 3

([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => [8,6,3] => 10010001000 => 00010001001 => 4

([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => [8,7] => 1010000000 => 0000000101 => 8

([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => [7,5,2] => 1001000100 => 0010001001 => 3

([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => [5,5,3] => 11001000 => 00010011 => 4

([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [8,2] => 1000000100 => 0010000001 => 3

([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => [7,4,4] => 1000110000 => 0000110001 => 5

([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => [6,4,3] => 100101000 => 000101001 => 4

([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => [7,5] => 100100000 => 000001001 => 6

([(1,5),(2,3),(3,5),(5,4)],6) => [8,8] => 1100000000 => 0000000011 => 9

([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => [8,2] => 1000000100 => 0010000001 => 3

([(1,5),(4,3),(5,2),(5,4)],6) => [8,8] => 1100000000 => 0000000011 => 9

([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => [6,6] => 11000000 => 00000011 => 7

([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => [8,6] => 1001000000 => 0000001001 => 7

([(1,5),(3,4),(4,2),(5,3)],6) => [6,6] => 11000000 => 00000011 => 7

([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [6,2] => 10000100 => 00100001 => 3

([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [5,3,3] => 10011000 => 00011001 => 4

([(0,5),(1,4),(4,2),(5,3)],6) => [4,4,4,4] => 11110000 => 00001111 => 5

([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => [6,4] => 10010000 => 00001001 => 5

([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => [4,3,3,2] => 10110100 => 00101101 => 3

([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [6,2] => 10000100 => 00100001 => 3

([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [6,4] => 10010000 => 00001001 => 5

([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => [7,5] => 100100000 => 000001001 => 6

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => [5,5,3,2,2] => 1100101100 => 0011010011 => 3

([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [3,2,2,2,2,2,2] => 1011111100 => 0011111101 => 3

([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => [5,4,2] => 10100100 => 00100101 => 3

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [5,2,2] => 10001100 => 00110001 => 3

([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => [5,5] => 1100000 => 0000011 => 6

([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => [5,3,3] => 10011000 => 00011001 => 4

([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => [5,5,3] => 11001000 => 00010011 => 4

([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [9] => 1000000000 => 0000000001 => 10

([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => [7,5] => 100100000 => 000001001 => 6

([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [7] => 10000000 => 00000001 => 8

([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => [7,5,5] => 1001100000 => 0000011001 => 6

([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1000000000 => 0000000001 => 10

([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [6,2] => 10000100 => 00100001 => 3

([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [9] => 1000000000 => 0000000001 => 10

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [7,6,6] => 1011000000 => 0000001101 => 7

([(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 => 001100011 => 3

([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => [5,5,4,2,2] => 1101001100 => 0011001011 => 3

([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => [5,3,3,2] => 100110100 => 001011001 => 3

([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => [5,5,2] => 11000100 => 00100011 => 3

([(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 => 001110001 => 3

([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => [5,5,2,2] => 110001100 => 001100011 => 3

([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => [6,5,4,2] => 1010100100 => 0010010101 => 3

([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => [6,5,5] => 101100000 => 000001101 => 6

([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7) => [8,8] => 1100000000 => 0000000011 => 9

([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => [6,5,5] => 101100000 => 000001101 => 6

([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => [6,5,3,3] => 1010011000 => 0001100101 => 4

([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => [6,5,3,3] => 1010011000 => 0001100101 => 4

([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => [4,4,4,4,4,4] => 1111110000 => 0000111111 => 5

([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => [6,4,2] => 100100100 => 001001001 => 3

([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [7,2] => 100000100 => 001000001 => 3

([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [7,2] => 100000100 => 001000001 => 3

([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => [5,3,3,2] => 100110100 => 001011001 => 3

([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7) => [5,5,3,2,2] => 1100101100 => 0011010011 => 3

([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) => [7,6,5] => 1010100000 => 0000010101 => 6

([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => [5,5,2] => 11000100 => 00100011 => 3

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => [5,2,2,2] => 100011100 => 001110001 => 3

([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => [5,3,3,2] => 100110100 => 001011001 => 3

([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => [5,5,2] => 11000100 => 00100011 => 3

([(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 => 001110001 => 3

([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => [5,5,2] => 11000100 => 00100011 => 3

([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7) => [6,5,4,2] => 1010100100 => 0010010101 => 3

([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => [7,6,5,2] => 10101000100 => 00100010101 => 3

([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7) => [7,6,5] => 1010100000 => 0000010101 => 6

([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => [5,2,2,2] => 100011100 => 001110001 => 3

([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => [5,3,3,2] => 100110100 => 001011001 => 3

([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => [6,4,2] => 100100100 => 001001001 => 3

([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => [5,5,4,2] => 110100100 => 001001011 => 3

([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [5,5,2,2] => 110001100 => 001100011 => 3

([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => [6,5,5] => 101100000 => 000001101 => 6

([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,5,4,2] => 1010100100 => 0010010101 => 3

([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => [6,5,5] => 101100000 => 000001101 => 6

([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => [6,5,3,3] => 1010011000 => 0001100101 => 4

([(0,3),(1,2),(1,5),(1,6),(3,5),(3,6),(5,4),(6,4)],7) => [5,5,3,2,2] => 1100101100 => 0011010011 => 3

([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => [5,5,2] => 11000100 => 00100011 => 3

([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [6,5] => 10100000 => 00000101 => 6

([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7) => [8,5] => 1000100000 => 0000010001 => 6

([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7) => [8,5] => 1000100000 => 0000010001 => 6

([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => [7,4] => 100010000 => 000010001 => 5

([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) => [6,4,2] => 100100100 => 001001001 => 3

([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => [5,5,3,2,2] => 1100101100 => 0011010011 => 3

([(0,5),(1,2),(1,3),(2,6),(3,6),(5,6),(6,4)],7) => [6,5,3,3] => 1010011000 => 0001100101 => 4

([(0,5),(1,3),(1,4),(3,6),(4,6),(5,2)],7) => [4,4,4,4,4,4] => 1111110000 => 0000111111 => 5

([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [7,2] => 100000100 => 001000001 => 3

([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(5,6)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(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 => 001100011 => 3

([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) => [6,4,2] => 100100100 => 001001001 => 3

([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => [6,3,3] => 100011000 => 000110001 => 4

([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => [6,5,4,2] => 1010100100 => 0010010101 => 3

([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7) => [5,5,2,2] => 110001100 => 001100011 => 3

([(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 => 001001011 => 3

([(0,4),(0,5),(1,3),(1,5),(3,6),(4,6),(5,6),(6,2)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(5,4),(6,4)],7) => [8,8] => 1100000000 => 0000000011 => 9

([(0,5),(0,6),(1,2),(1,3),(1,5),(2,6),(3,6),(6,4)],7) => [7,6,5] => 1010100000 => 0000010101 => 6

([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,2),(0,3),(0,4),(1,5),(1,6),(2,6),(3,5),(3,6),(4,1)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,4),(0,5),(0,6),(1,2),(1,3),(2,6),(3,4),(3,5),(3,6)],7) => [7,6,5,2] => 10101000100 => 00100010101 => 3

([(0,5),(0,6),(1,2),(1,3),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,2),(0,3),(1,5),(1,6),(2,6),(3,5),(5,4),(6,4)],7) => [8,8] => 1100000000 => 0000000011 => 9

([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,5),(1,4),(1,6),(5,6),(6,2),(6,3)],7) => [5,5,3,2,2] => 1100101100 => 0011010011 => 3

([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => [8,5] => 1000100000 => 0000010001 => 6

([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [6,5] => 10100000 => 00000101 => 6

([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) => [9,4] => 10000010000 => 00001000001 => 5

([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [6,4,2] => 100100100 => 001001001 => 3

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(1,6),(2,3),(3,5),(3,6),(6,4)],7) => [6,6,6,6] => 1111000000 => 0000001111 => 7

([(0,6),(1,5),(3,6),(5,2),(5,3),(6,4)],7) => [6,4,4,2] => 1001100100 => 0010011001 => 3

([(2,6),(4,5),(5,3),(6,4)],7) => [6,6,6,6] => 1111000000 => 0000001111 => 7

([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7) => [5,3,3,2] => 100110100 => 001011001 => 3

([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [5,3,3,2] => 100110100 => 001011001 => 3

([(0,6),(1,5),(5,4),(6,2),(6,3)],7) => [4,4,4,4,4,4] => 1111110000 => 0000111111 => 5

([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [10] => 10000000000 => 00000000001 => 11

([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7) => [6,4,2] => 100100100 => 001001001 => 3

([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => [8,5] => 1000100000 => 0000010001 => 6

([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => [5,5,2] => 11000100 => 00100011 => 3

([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) => [8,5] => 1000100000 => 0000010001 => 6

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [5,5,4,2,2] => 1101001100 => 0011001011 => 3

([(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => [6,5] => 10100000 => 00000101 => 6

([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3),(5,4)],7) => [6,5,5] => 101100000 => 000001101 => 6

([(0,5),(0,6),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5)],7) => [7,6,5] => 1010100000 => 0000010101 => 6

([(0,5),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4)],7) => [6,5,5] => 101100000 => 000001101 => 6

([(0,3),(1,4),(1,5),(1,6),(2,6),(3,2),(3,4),(3,5)],7) => [7,6,5] => 1010100000 => 0000010101 => 6

([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => [5,4,4,4] => 101110000 => 000011101 => 5

([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7) => [7,5,4] => 1001010000 => 0000101001 => 5

([(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2)],7) => [8,8] => 1100000000 => 0000000011 => 9

([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [10] => 10000000000 => 00000000001 => 11

([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,4),(2,5),(2,6),(3,1),(3,5),(3,6),(4,2),(4,3)],7) => [5,5,2,2] => 110001100 => 001100011 => 3

([(0,5),(0,6),(1,3),(1,5),(1,6),(3,4),(4,2),(6,4)],7) => [5,5,4,2] => 110100100 => 001001011 => 3

([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(4,3),(5,4),(6,3)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) => [8,5] => 1000100000 => 0000010001 => 6

([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,5),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4)],7) => [8,5,2] => 10001000100 => 00100010001 => 3

([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7) => [6,5,5] => 101100000 => 000001101 => 6

([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) => [9,4] => 10000010000 => 00001000001 => 5

([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [6,2,2] => 100001100 => 001100001 => 3

([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => [6,5] => 10100000 => 00000101 => 6

([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7) => [7,5,4] => 1001010000 => 0000101001 => 5

([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,6),(4,3),(5,1),(5,2),(6,4),(6,5)],7) => [6,5,3,3] => 1010011000 => 0001100101 => 4

([(0,3),(0,5),(1,6),(2,6),(4,2),(5,1),(5,4)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,6),(1,4),(4,5),(5,2),(5,3),(5,6)],7) => [7,6,5] => 1010100000 => 0000010101 => 6

([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [7,2] => 100000100 => 001000001 => 3

([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => [7,4] => 100010000 => 000010001 => 5

([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => [6,6,6] => 111000000 => 000000111 => 7

([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => [6,3,3] => 100011000 => 000110001 => 4

([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [10] => 10000000000 => 00000000001 => 11

([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7) => [6,5,3] => 101001000 => 000100101 => 4

([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 100000000 => 000000001 => 9

([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 10000000000 => 00000000001 => 11

([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) => [9,8] => 10100000000 => 00000000101 => 9

([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [10] => 10000000000 => 00000000001 => 11

([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => [6,3,3] => 100011000 => 000110001 => 4

([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [6,3,3] => 100011000 => 000110001 => 4

([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(5,4)],7) => [6,5,3,3] => 1010011000 => 0001100101 => 4

([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [7,2] => 100000100 => 001000001 => 3

([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [7,4] => 100010000 => 000010001 => 5

([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [7,6] => 101000000 => 000000101 => 7

([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [7,2] => 100000100 => 001000001 => 3

([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [5,4,4,4] => 101110000 => 000011101 => 5

([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => [7,4] => 100010000 => 000010001 => 5

([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => [8,6,2] => 10010000100 => 00100001001 => 3

([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [7,5] => 100100000 => 000001001 => 6

([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => [7,6,3] => 1010001000 => 0001000101 => 4

([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => [8,7] => 1010000000 => 0000000101 => 8

([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [8,8] => 1100000000 => 0000000011 => 9

([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [8,8] => 1100000000 => 0000000011 => 9

([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [9,8] => 10100000000 => 00000000101 => 9

([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [9,8] => 10100000000 => 00000000101 => 9

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$F_{1} = q^{3}$

$F_{2} = q^{3} + q^{4}$

$F_{3} = 3\ q^{3} + q^{5} + q^{7}$

Description

The position of the first one in a binary word after appending a 1 at the end.
Regarding the binary word as a subset of

$\{1,\dots,n,n+1\}$ that contains

$n+1$ , this is the minimal element of the set.

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

reverse

Description

Return the reversal of a binary word.