- FindStat

Identifier

Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
St000983: Binary words ⟶ ℤ

Values

([(0,1)],2) => [1] => 10 => 01 => 2

([(1,2)],3) => [1] => 10 => 01 => 2

([(0,2),(1,2)],3) => [1,1] => 110 => 011 => 2

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

([(2,3)],4) => [1] => 10 => 01 => 2

([(1,3),(2,3)],4) => [1,1] => 110 => 011 => 2

([(0,3),(1,3),(2,3)],4) => [1,1,1] => 1110 => 0111 => 2

([(0,3),(1,2)],4) => [1,1] => 110 => 011 => 2

([(0,3),(1,2),(2,3)],4) => [1,1,1] => 1110 => 0111 => 2

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

([(0,3),(1,2),(1,3),(2,3)],4) => [3,1] => 10010 => 01001 => 3

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

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

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

([(3,4)],5) => [1] => 10 => 01 => 2

([(2,4),(3,4)],5) => [1,1] => 110 => 011 => 2

([(1,4),(2,4),(3,4)],5) => [1,1,1] => 1110 => 0111 => 2

([(0,4),(1,4),(2,4),(3,4)],5) => [1,1,1,1] => 11110 => 01111 => 2

([(1,4),(2,3)],5) => [1,1] => 110 => 011 => 2

([(1,4),(2,3),(3,4)],5) => [1,1,1] => 1110 => 0111 => 2

([(0,1),(2,4),(3,4)],5) => [1,1,1] => 1110 => 0111 => 2

([(2,3),(2,4),(3,4)],5) => [3] => 1000 => 0001 => 2

([(0,4),(1,4),(2,3),(3,4)],5) => [1,1,1,1] => 11110 => 01111 => 2

([(1,4),(2,3),(2,4),(3,4)],5) => [3,1] => 10010 => 01001 => 3

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [3,1,1] => 100110 => 011001 => 2

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

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [4,1] => 100010 => 010001 => 3

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

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,1,1] => 100110 => 011001 => 2

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5,1] => 1000010 => 0100001 => 3

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

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

([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1] => 11110 => 01111 => 2

([(0,1),(2,3),(2,4),(3,4)],5) => [3,1] => 10010 => 01001 => 3

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => [3,1,1] => 100110 => 011001 => 2

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => [3,3] => 11000 => 00011 => 2

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

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

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

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => [5,1] => 1000010 => 0100001 => 3

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

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [6,1] => 10000010 => 01000001 => 3

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

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

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

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

([(4,5)],6) => [1] => 10 => 01 => 2

([(3,5),(4,5)],6) => [1,1] => 110 => 011 => 2

([(2,5),(3,5),(4,5)],6) => [1,1,1] => 1110 => 0111 => 2

([(1,5),(2,5),(3,5),(4,5)],6) => [1,1,1,1] => 11110 => 01111 => 2

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [1,1,1,1,1] => 111110 => 011111 => 2

([(2,5),(3,4)],6) => [1,1] => 110 => 011 => 2

([(2,5),(3,4),(4,5)],6) => [1,1,1] => 1110 => 0111 => 2

([(1,2),(3,5),(4,5)],6) => [1,1,1] => 1110 => 0111 => 2

([(3,4),(3,5),(4,5)],6) => [3] => 1000 => 0001 => 2

([(1,5),(2,5),(3,4),(4,5)],6) => [1,1,1,1] => 11110 => 01111 => 2

([(0,1),(2,5),(3,5),(4,5)],6) => [1,1,1,1] => 11110 => 01111 => 2

([(2,5),(3,4),(3,5),(4,5)],6) => [3,1] => 10010 => 01001 => 3

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [1,1,1,1,1] => 111110 => 011111 => 2

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1] => 100110 => 011001 => 2

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 1001110 => 0111001 => 2

([(2,4),(2,5),(3,4),(3,5)],6) => [4] => 10000 => 00001 => 2

([(0,5),(1,5),(2,4),(3,4)],6) => [1,1,1,1] => 11110 => 01111 => 2

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [4,1] => 100010 => 010001 => 3

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [1,1,1,1,1] => 111110 => 011111 => 2

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

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,1,1] => 100110 => 011001 => 2

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [1,1,1,1,1] => 111110 => 011111 => 2

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [4,1,1] => 1000110 => 0110001 => 2

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 1000010 => 0100001 => 3

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1,1] => 10000110 => 01100001 => 2

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

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [4,1,1] => 1000110 => 0110001 => 2

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6,1] => 10000010 => 01000001 => 3

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

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1,1] => 10000110 => 01100001 => 2

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [7,1] => 100000010 => 010000001 => 3

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

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

([(0,5),(1,4),(2,3)],6) => [1,1,1] => 1110 => 0111 => 2

([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1] => 11110 => 01111 => 2

([(0,1),(2,5),(3,4),(4,5)],6) => [1,1,1,1] => 11110 => 01111 => 2

([(1,2),(3,4),(3,5),(4,5)],6) => [3,1] => 10010 => 01001 => 3

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [1,1,1,1,1] => 111110 => 011111 => 2

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,1,1] => 100110 => 011001 => 2

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1] => 100110 => 011001 => 2

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,1,1,1] => 1001110 => 0111001 => 2

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3] => 11000 => 00011 => 2

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,1] => 110010 => 010011 => 3

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

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [4,1,1] => 1000110 => 0110001 => 2

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

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [5,1] => 1000010 => 0100001 => 3

([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [5,1] => 1000010 => 0100001 => 3

([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [6,1] => 10000010 => 01000001 => 3

([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1,1] => 10000110 => 01100001 => 2

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

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [7,1] => 100000010 => 010000001 => 3

([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1] => 111110 => 011111 => 2

>>> Load all 485 entries. <<<

([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,1] => 100010 => 010001 => 3

([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,1,1] => 100110 => 011001 => 2

([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [4,1,1] => 1000110 => 0110001 => 2

([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 1000010 => 0100001 => 3

([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => [4,3] => 101000 => 000101 => 4

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => [5,1,1] => 10000110 => 01100001 => 2

([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,1] => 110010 => 010011 => 3

([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,3] => 1001000 => 0001001 => 3

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

([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [5,1,1] => 10000110 => 01100001 => 2

([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1] => 10000010 => 01000001 => 3

([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1,1] => 100000110 => 011000001 => 2

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

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

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [7,1] => 100000010 => 010000001 => 3

([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [7,1] => 100000010 => 010000001 => 3

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

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

([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [7,1] => 100000010 => 010000001 => 3

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

([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1,1] => 100000110 => 011000001 => 2

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

([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [6,1] => 10000010 => 01000001 => 3

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

([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [7,1] => 100000010 => 010000001 => 3

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

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

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

([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [6,1] => 10000010 => 01000001 => 3

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

([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [5,1,1] => 10000110 => 01100001 => 2

([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [6,1] => 10000010 => 01000001 => 3

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

([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [7,1] => 100000010 => 010000001 => 3

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

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

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

([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [7,1] => 100000010 => 010000001 => 3

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

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

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

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

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

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

([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => 11000 => 00011 => 2

([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => [5,1,1] => 10000110 => 01100001 => 2

([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => [3,3,1] => 110010 => 010011 => 3

([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1] => 10000010 => 01000001 => 3

([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [5,3] => 1001000 => 0001001 => 3

([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1,1] => 100000110 => 011000001 => 2

([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,3] => 10001000 => 00010001 => 3

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

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

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

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

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

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

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

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

([(5,6)],7) => [1] => 10 => 01 => 2

([(4,6),(5,6)],7) => [1,1] => 110 => 011 => 2

([(3,6),(4,6),(5,6)],7) => [1,1,1] => 1110 => 0111 => 2

([(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1] => 11110 => 01111 => 2

([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(3,6),(4,5)],7) => [1,1] => 110 => 011 => 2

([(3,6),(4,5),(5,6)],7) => [1,1,1] => 1110 => 0111 => 2

([(2,3),(4,6),(5,6)],7) => [1,1,1] => 1110 => 0111 => 2

([(4,5),(4,6),(5,6)],7) => [3] => 1000 => 0001 => 2

([(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1] => 11110 => 01111 => 2

([(1,2),(3,6),(4,6),(5,6)],7) => [1,1,1,1] => 11110 => 01111 => 2

([(3,6),(4,5),(4,6),(5,6)],7) => [3,1] => 10010 => 01001 => 3

([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1] => 100110 => 011001 => 2

([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(3,5),(3,6),(4,5),(4,6)],7) => [4] => 10000 => 00001 => 2

([(1,6),(2,6),(3,5),(4,5)],7) => [1,1,1,1] => 11110 => 01111 => 2

([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [4,1] => 100010 => 010001 => 3

([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5] => 100000 => 000001 => 2

([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,1,1] => 100110 => 011001 => 2

([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [4,1,1] => 1000110 => 0110001 => 2

([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1] => 1000010 => 0100001 => 3

([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

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

([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1] => 1000110 => 0110001 => 2

([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1] => 10000010 => 01000001 => 3

([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

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

([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

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

([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,6),(2,5),(3,4)],7) => [1,1,1] => 1110 => 0111 => 2

([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1] => 11110 => 01111 => 2

([(1,2),(3,6),(4,5),(5,6)],7) => [1,1,1,1] => 11110 => 01111 => 2

([(0,3),(1,2),(4,6),(5,6)],7) => [1,1,1,1] => 11110 => 01111 => 2

([(2,3),(4,5),(4,6),(5,6)],7) => [3,1] => 10010 => 01001 => 3

([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,1,1] => 100110 => 011001 => 2

([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1] => 100110 => 011001 => 2

([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3] => 11000 => 00011 => 2

([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1] => 110010 => 010011 => 3

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5] => 100000 => 000001 => 2

([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [4,1,1] => 1000110 => 0110001 => 2

([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

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

([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => [5,1] => 1000010 => 0100001 => 3

([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1] => 1000010 => 0100001 => 3

([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6,1] => 10000010 => 01000001 => 3

([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

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

([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,1] => 100010 => 010001 => 3

([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,1,1] => 100110 => 011001 => 2

([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [4,1,1] => 1000110 => 0110001 => 2

([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1] => 1000110 => 0110001 => 2

([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1] => 1000010 => 0100001 => 3

([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [4,3] => 101000 => 000101 => 4

([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1] => 110010 => 010011 => 3

([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [4,3,1] => 1010010 => 0100101 => 4

([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3] => 1001000 => 0001001 => 3

([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

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

([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 10000010 => 01000001 => 3

([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

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

([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

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

([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

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

([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1] => 10000010 => 01000001 => 3

([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,3,1] => 1010010 => 0100101 => 4

([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,3] => 10001000 => 00010001 => 3

([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,3] => 100001000 => 000100001 => 3

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

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

([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1] => 10000010 => 01000001 => 3

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

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

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

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

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

([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => [6,1] => 10000010 => 01000001 => 3

([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [6,1] => 10000010 => 01000001 => 3

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

([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [6,1] => 10000010 => 01000001 => 3

([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

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

([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

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

([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,1,1] => 1000110 => 0110001 => 2

([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => [4,4] => 110000 => 000011 => 2

([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,1] => 1010010 => 0100101 => 4

([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(0,1),(0,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4] => 1010000 => 0000101 => 4

([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [5,5] => 1100000 => 0000011 => 2

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

([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

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

([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1] => 111110 => 011111 => 2

([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,1,1] => 100110 => 011001 => 2

([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1] => 110010 => 010011 => 3

([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,3] => 111000 => 000111 => 2

([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1] => 1111110 => 0111111 => 2

([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5,1] => 1000010 => 0100001 => 3

([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,1,1,1] => 1001110 => 0111001 => 2

([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [4,1,1,1] => 10001110 => 01110001 => 2

([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6,1] => 10000010 => 01000001 => 3

([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 01111001 => 2

([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [4,3,1] => 1010010 => 0100101 => 4

([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [5,3] => 1001000 => 0001001 => 3

([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6,3] => 10001000 => 00010001 => 3

([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,3] => 100001000 => 000100001 => 3

([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => 11000 => 00011 => 2

([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 10000110 => 01100001 => 2

([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,1] => 110010 => 010011 => 3

([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,3,1] => 110010 => 010011 => 3

([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 10000010 => 01000001 => 3

([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,3] => 1001000 => 0001001 => 3

([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3] => 10001000 => 00010001 => 3

([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3,1] => 100010010 => 010010001 => 3

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

([(0,1),(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

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

([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [6,3] => 10001000 => 00010001 => 3

([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3] => 111000 => 000111 => 2

([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [7,3] => 100001000 => 000100001 => 3

([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [7,3] => 100001000 => 000100001 => 3

([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3,1] => 100010010 => 010010001 => 3

([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,3] => 1000001000 => 0001000001 => 3

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

([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

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

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

([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,6),(1,2),(1,6),(2,4),(3,4),(3,5),(4,5),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,1),(0,2),(1,6),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(4,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [7,1] => 100000010 => 010000001 => 3

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

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

([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7) => [4,3,1] => 1010010 => 0100101 => 4

([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1] => 100000010 => 010000001 => 3

([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,3] => 10001000 => 00010001 => 3

([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [6,3] => 10001000 => 00010001 => 3

([(0,1),(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,3] => 100001000 => 000100001 => 3

([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [8,3] => 1000001000 => 0001000001 => 3

([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7,3] => 100001000 => 000100001 => 3

([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,3] => 100001000 => 000100001 => 3

([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,3] => 100001000 => 000100001 => 3

([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,3] => 1000001000 => 0001000001 => 3

([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,3] => 1000001000 => 0001000001 => 3

([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [4,3] => 101000 => 000101 => 4

([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => 100000110 => 011000001 => 2

([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,1,1] => 1100110 => 0110011 => 2

([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3] => 1001000 => 0001001 => 3

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [5,1,1,1] => 100001110 => 011100001 => 2

([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,4] => 1010000 => 0000101 => 4

([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,4] => 10010000 => 00001001 => 3

([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5] => 1100000 => 0000011 => 2

([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [6,3,1] => 100010010 => 010010001 => 3

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

([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,2),(0,6),(1,2),(1,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,4),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [9] => 1000000000 => 0000000001 => 2

([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [5,3,1] => 10010010 => 01001001 => 3

([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3] => 10001000 => 00010001 => 3

([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,5] => 1100000 => 0000011 => 2

([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [6,3,1] => 100010010 => 010010001 => 3

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

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

([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [8,3] => 1000001000 => 0001000001 => 3

search for individual values

searching the database for the individual values of this statistic

Description

The length of the longest alternating subword.
This is the length of the longest consecutive subword of the form $010...$ or of the form $101...$.

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

to edge-partition of biconnected components

Description

Sends a graph to the partition recording the number of edges in its biconnected components.
The biconnected components are also known as blocks of a graph.

Map

reverse

Description

Return the reversal of a binary word.