Identifier
-
Mp00317:
Integer partitions
—odd parts⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001581: Graphs ⟶ ℤ
Values
[1] => 1 => [1,1] => ([(0,1)],2) => 2
[2] => 0 => [2] => ([],2) => 1
[1,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[3] => 1 => [1,1] => ([(0,1)],2) => 2
[2,1] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[4] => 0 => [2] => ([],2) => 1
[3,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[2,2] => 00 => [3] => ([],3) => 1
[2,1,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5] => 1 => [1,1] => ([(0,1)],2) => 2
[4,1] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[3,2] => 10 => [1,2] => ([(1,2)],3) => 2
[3,1,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[2,2,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[2,1,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[1,1,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6] => 0 => [2] => ([],2) => 1
[5,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[4,2] => 00 => [3] => ([],3) => 1
[4,1,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[3,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[3,2,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[3,1,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[2,2,2] => 000 => [4] => ([],4) => 1
[2,2,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[2,1,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[1,1,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[7] => 1 => [1,1] => ([(0,1)],2) => 2
[6,1] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[5,2] => 10 => [1,2] => ([(1,2)],3) => 2
[5,1,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[4,3] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[4,2,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,1,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[3,3,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[3,2,2] => 100 => [1,3] => ([(2,3)],4) => 2
[3,2,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[3,1,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,2,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,2,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[2,1,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[8] => 0 => [2] => ([],2) => 1
[7,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[6,2] => 00 => [3] => ([],3) => 1
[6,1,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[5,2,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,1,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[4,4] => 00 => [3] => ([],3) => 1
[4,3,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[4,2,2] => 000 => [4] => ([],4) => 1
[4,2,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,1,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,3,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[3,3,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[3,2,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[3,2,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,1,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[2,2,2,2] => 0000 => [5] => ([],5) => 1
[2,2,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,2,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[9] => 1 => [1,1] => ([(0,1)],2) => 2
[8,1] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[7,2] => 10 => [1,2] => ([(1,2)],3) => 2
[7,1,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[6,3] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[6,2,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,1,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,4] => 10 => [1,2] => ([(1,2)],3) => 2
[5,3,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[5,2,2] => 100 => [1,3] => ([(2,3)],4) => 2
[5,2,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,1,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,4,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,3,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[4,3,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,2,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,2,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[3,3,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[3,3,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[3,3,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,2,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[3,2,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[3,2,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,2,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,2,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[10] => 0 => [2] => ([],2) => 1
[9,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[8,2] => 00 => [3] => ([],3) => 1
[8,1,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,2,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,1,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[6,4] => 00 => [3] => ([],3) => 1
[6,3,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,2,2] => 000 => [4] => ([],4) => 1
[6,2,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,1,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
>>> Load all 834 entries. <<<[5,5] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[5,4,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,3,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[5,3,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,2,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,2,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,1,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[4,4,2] => 000 => [4] => ([],4) => 1
[4,4,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,3] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[4,3,2,1] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,2,2,2] => 0000 => [5] => ([],5) => 1
[4,2,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[3,3,3,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[3,3,2,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,3,2,1,1] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,3,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[3,2,2,2,1] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,2,1,1,1] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[2,2,2,2,2] => 00000 => [6] => ([],6) => 1
[2,2,2,2,1,1] => 000011 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[11] => 1 => [1,1] => ([(0,1)],2) => 2
[10,1] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[9,2] => 10 => [1,2] => ([(1,2)],3) => 2
[9,1,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[8,3] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[8,2,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,1,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,4] => 10 => [1,2] => ([(1,2)],3) => 2
[7,3,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[7,2,2] => 100 => [1,3] => ([(2,3)],4) => 2
[7,2,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,1,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,5] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[6,4,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,3,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[6,3,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[6,2,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[6,2,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,5,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[5,4,2] => 100 => [1,3] => ([(2,3)],4) => 2
[5,4,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,3,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[5,3,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,3,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,2,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[5,2,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[4,4,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,4,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,4,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,3,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,3,2,2] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[4,3,2,1,1] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[4,2,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,2,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,3,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[3,3,3,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,3,2,2,1] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[3,3,2,1,1,1] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[3,2,2,2,2] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,2,2,2,1,1] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,2,2,2,2,1] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,2,2,2,1,1,1] => 0000111 => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[12] => 0 => [2] => ([],2) => 1
[11,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[10,2] => 00 => [3] => ([],3) => 1
[10,1,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[9,2,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,1,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[8,4] => 00 => [3] => ([],3) => 1
[8,3,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[8,2,2] => 000 => [4] => ([],4) => 1
[8,2,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,1,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[7,5] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,4,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,3,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,3,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[7,2,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,2,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[7,1,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[6,6] => 00 => [3] => ([],3) => 1
[6,5,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,4,2] => 000 => [4] => ([],4) => 1
[6,4,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,3,3] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,3,2,1] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,3,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,2,2,2] => 0000 => [5] => ([],5) => 1
[6,2,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[5,5,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[5,5,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,4,3] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[5,4,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,3,3,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,3,2,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,3,2,1,1] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,3,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[5,2,2,2,1] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,2,1,1,1] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[4,4,4] => 000 => [4] => ([],4) => 1
[4,4,3,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,4,2,2] => 0000 => [5] => ([],5) => 1
[4,4,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,4,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[4,3,3,2] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,3,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,3,2,2,1] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,1,1,1] => 010111 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[4,2,2,2,2] => 00000 => [6] => ([],6) => 1
[4,2,2,2,1,1] => 000011 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,3,3,3] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[3,3,3,2,1] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,3,3,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[3,3,2,2,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,3,2,2,1,1] => 110011 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[3,2,2,2,2,1] => 100001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,2,2,2,2,2] => 000000 => [7] => ([],7) => 1
[2,2,2,2,2,1,1] => 0000011 => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[13] => 1 => [1,1] => ([(0,1)],2) => 2
[12,1] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[11,2] => 10 => [1,2] => ([(1,2)],3) => 2
[11,1,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[10,3] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[10,2,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[10,1,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[9,4] => 10 => [1,2] => ([(1,2)],3) => 2
[9,3,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[9,2,2] => 100 => [1,3] => ([(2,3)],4) => 2
[9,2,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[9,1,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[8,5] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[8,4,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,3,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[8,3,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[8,2,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[8,2,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[8,1,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[7,6] => 10 => [1,2] => ([(1,2)],3) => 2
[7,5,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[7,4,2] => 100 => [1,3] => ([(2,3)],4) => 2
[7,4,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,3,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[7,3,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,3,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[7,2,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[7,2,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[7,2,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[6,6,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,5,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[6,5,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[6,4,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,4,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[6,4,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,3,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[6,3,2,2] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[6,3,2,1,1] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[6,2,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,5,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[5,5,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,5,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,4,4] => 100 => [1,3] => ([(2,3)],4) => 2
[5,4,3,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,4,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[5,4,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,3,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,3,3,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,3,2,2,1] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,2,1,1,1] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,2,2,2,2] => 10000 => [1,5] => ([(4,5)],6) => 2
[5,2,2,2,1,1] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,4,4,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,4,3,2] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,4,3,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,4,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,4,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,3,3] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,3,3,2,1] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,3,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[4,3,2,2,2] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,2,2,1,1] => 010011 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,2,2,2,1] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,2,2,2,1,1,1] => 0000111 => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[3,3,3,3,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,3,3,2,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[3,3,3,2,1,1] => 111011 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[3,3,2,2,2,1] => 110001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,2,2,2,2,2] => 100000 => [1,6] => ([(5,6)],7) => 2
[3,2,2,2,2,1,1] => 1000011 => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[2,2,2,2,2,2,1] => 0000001 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[14] => 0 => [2] => ([],2) => 1
[13,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[12,2] => 00 => [3] => ([],3) => 1
[12,1,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[11,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[11,2,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[11,1,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[10,4] => 00 => [3] => ([],3) => 1
[10,3,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[10,2,2] => 000 => [4] => ([],4) => 1
[10,2,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[10,1,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[9,5] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[9,4,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,3,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[9,3,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[9,2,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[9,2,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[9,1,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[8,6] => 00 => [3] => ([],3) => 1
[8,5,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[8,4,2] => 000 => [4] => ([],4) => 1
[8,4,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,3,3] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[8,3,2,1] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,3,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[8,2,2,2] => 0000 => [5] => ([],5) => 1
[8,2,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[8,2,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,7] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[7,6,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,5,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,5,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[7,4,3] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,4,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,4,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[7,3,3,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[7,3,2,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[7,3,2,1,1] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[7,3,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[7,2,2,2,1] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,2,2,1,1,1] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,6,2] => 000 => [4] => ([],4) => 1
[6,6,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,5,3] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,5,2,1] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,5,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,4] => 000 => [4] => ([],4) => 1
[6,4,3,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,4,2,2] => 0000 => [5] => ([],5) => 1
[6,4,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,4,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,3,3,2] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,3,3,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,3,2,2,1] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,2,1,1,1] => 010111 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,2,2,2,2] => 00000 => [6] => ([],6) => 1
[6,2,2,2,1,1] => 000011 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,5,4] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[5,5,3,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,5,2,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,5,2,1,1] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,5,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[5,4,4,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,3,2] => 1010 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,3,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,2,2,1] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,2,1,1,1] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[5,3,3,3] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,3,3,2,1] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,3,3,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[5,3,2,2,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,3,2,2,1,1] => 110011 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[5,2,2,2,2,1] => 100001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,4,4,2] => 0000 => [5] => ([],5) => 1
[4,4,4,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,4,3,3] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,4,3,2,1] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,4,3,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[4,4,2,2,2] => 00000 => [6] => ([],6) => 1
[4,4,2,2,1,1] => 000011 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,3,3,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,3,3,2,2] => 01100 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,3,2,1,1] => 011011 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[4,3,2,2,2,1] => 010001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,2,2,2,2] => 000000 => [7] => ([],7) => 1
[4,2,2,2,2,1,1] => 0000011 => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[3,3,3,3,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,3,3,3,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[3,3,3,2,2,1] => 111001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[3,3,2,2,2,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[3,3,2,2,2,1,1] => 1100011 => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5
[3,2,2,2,2,2,1] => 1000001 => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[2,2,2,2,2,2,2] => 0000000 => [8] => ([],8) => 1
[15] => 1 => [1,1] => ([(0,1)],2) => 2
[14,1] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[13,2] => 10 => [1,2] => ([(1,2)],3) => 2
[13,1,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[12,3] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[12,2,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[12,1,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[11,4] => 10 => [1,2] => ([(1,2)],3) => 2
[11,3,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[11,2,2] => 100 => [1,3] => ([(2,3)],4) => 2
[11,2,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[11,1,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[10,5] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[10,4,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[10,3,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[10,3,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[10,2,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[10,2,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[10,1,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[9,6] => 10 => [1,2] => ([(1,2)],3) => 2
[9,5,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[9,4,2] => 100 => [1,3] => ([(2,3)],4) => 2
[9,4,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[9,3,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[9,3,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[9,3,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[9,2,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[9,2,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[9,2,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[8,7] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[8,6,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,5,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[8,5,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[8,4,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,4,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[8,4,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[8,3,3,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[8,3,2,2] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[8,3,2,1,1] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[8,3,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[8,2,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[8,2,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,7,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[7,6,2] => 100 => [1,3] => ([(2,3)],4) => 2
[7,6,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,5,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[7,5,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,5,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[7,4,4] => 100 => [1,3] => ([(2,3)],4) => 2
[7,4,3,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,4,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[7,4,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[7,4,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[7,3,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,3,3,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[7,3,2,2,1] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[7,3,2,1,1,1] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[7,2,2,2,2] => 10000 => [1,5] => ([(4,5)],6) => 2
[7,2,2,2,1,1] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,6,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,6,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[6,6,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,5,4] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[6,5,3,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[6,5,2,2] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[6,5,2,1,1] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,5,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[6,4,4,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[6,4,3,2] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[6,4,3,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,4,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,3,3] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[6,3,3,2,1] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,3,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[6,3,2,2,2] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,2,2,1,1] => 010011 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,2,2,2,1] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[6,2,2,2,1,1,1] => 0000111 => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[5,5,5] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[5,5,4,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,5,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,5,3,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,5,2,2,1] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,5,2,1,1,1] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,4,4,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[5,4,4,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,3,3] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,4,3,2,1] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,3,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,4,2,2,2] => 10000 => [1,5] => ([(4,5)],6) => 2
[5,4,2,2,1,1] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,3,3,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,3,3,2,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,3,2,1,1] => 111011 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,3,2,2,2,1] => 110001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,2,2,2,2] => 100000 => [1,6] => ([(5,6)],7) => 2
[5,2,2,2,2,1,1] => 1000011 => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[4,4,4,3] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,4,4,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,4,4,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,4,3,3,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,4,3,2,2] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,4,3,2,1,1] => 001011 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,4,2,2,2,1] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,4,2,2,1,1,1] => 0000111 => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[4,3,3,3,2] => 01110 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,3,3,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[4,3,3,2,2,1] => 011001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,2,2,2,2] => 010000 => [2,5] => ([(4,6),(5,6)],7) => 2
[4,3,2,2,2,1,1] => 0100011 => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[4,2,2,2,2,2,1] => 0000001 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,3,3,3,3] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,3,3,3,2,1] => 111101 => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[3,3,3,2,2,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,3,2,2,2,2,1] => 1100001 => [1,1,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[3,2,2,2,2,2,2] => 1000000 => [1,7] => ([(6,7)],8) => 2
[16] => 0 => [2] => ([],2) => 1
[15,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[14,2] => 00 => [3] => ([],3) => 1
[14,1,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[13,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[13,2,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[13,1,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[12,4] => 00 => [3] => ([],3) => 1
[12,3,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[12,2,2] => 000 => [4] => ([],4) => 1
[12,2,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[12,1,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[11,5] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[11,4,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[11,3,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[11,3,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[11,2,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[11,2,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[11,1,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[10,6] => 00 => [3] => ([],3) => 1
[10,5,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[10,4,2] => 000 => [4] => ([],4) => 1
[10,4,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[10,3,3] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[10,3,2,1] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[10,3,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[10,2,2,2] => 0000 => [5] => ([],5) => 1
[10,2,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[10,2,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[9,7] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[9,6,1] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,5,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[9,5,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[9,4,3] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[9,4,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[9,4,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[9,3,3,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[9,3,2,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[9,3,2,1,1] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[9,3,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[9,2,2,2,1] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[9,2,2,1,1,1] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[8,8] => 00 => [3] => ([],3) => 1
[8,7,1] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[8,6,2] => 000 => [4] => ([],4) => 1
[8,6,1,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,5,3] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[8,5,2,1] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,5,1,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[8,4,4] => 000 => [4] => ([],4) => 1
[8,4,3,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,4,2,2] => 0000 => [5] => ([],5) => 1
[8,4,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[8,4,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[8,3,3,2] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[8,3,3,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[8,3,2,2,1] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[8,3,2,1,1,1] => 010111 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[8,2,2,2,2] => 00000 => [6] => ([],6) => 1
[8,2,2,2,1,1] => 000011 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,7,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,7,1,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[7,6,3] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
[7,6,2,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,6,1,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[7,5,4] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[7,5,3,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[7,5,2,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[7,5,2,1,1] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[7,5,1,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[7,4,4,1] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,4,3,2] => 1010 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3
[7,4,3,1,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[7,4,2,2,1] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[7,4,2,1,1,1] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,3,3,3] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[7,3,3,2,1] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[7,3,3,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[7,3,2,2,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[7,3,2,2,1,1] => 110011 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,2,2,2,2,1] => 100001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,6,4] => 000 => [4] => ([],4) => 1
[6,6,3,1] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,6,2,2] => 0000 => [5] => ([],5) => 1
[6,6,2,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,6,1,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,5] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[6,5,4,1] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,5,3,2] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,5,3,1,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,2,2,1] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,5,2,1,1,1] => 010111 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,4,2] => 0000 => [5] => ([],5) => 1
[6,4,4,1,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,4,3,3] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[6,4,3,2,1] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,4,3,1,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,2,2,2] => 00000 => [6] => ([],6) => 1
[6,4,2,2,1,1] => 000011 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,3,3,1] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,3,3,2,2] => 01100 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,3,2,1,1] => 011011 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,3,2,2,2,1] => 010001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,2,2,2,2] => 000000 => [7] => ([],7) => 1
[6,2,2,2,2,1,1] => 0000011 => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[5,5,5,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,5,4,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,5,4,1,1] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,5,3,3] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,5,3,2,1] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,5,3,1,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[5,5,2,2,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,5,2,2,1,1] => 110011 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[5,4,4,3] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,4,2,1] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,4,1,1,1] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[5,4,3,3,1] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,3,2,2] => 10100 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,3,2,1,1] => 101011 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[5,4,2,2,2,1] => 100001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,3,3,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,3,3,3,1,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[5,3,3,2,2,1] => 111001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[5,3,2,2,2,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[5,3,2,2,2,1,1] => 1100011 => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5
[5,2,2,2,2,2,1] => 1000001 => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3
[4,4,4,4] => 0000 => [5] => ([],5) => 1
[4,4,4,3,1] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,4,4,2,2] => 00000 => [6] => ([],6) => 1
[4,4,4,2,1,1] => 000011 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,4,3,3,2] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,4,3,3,1,1] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[4,4,3,2,2,1] => 001001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,4,2,2,2,2] => 000000 => [7] => ([],7) => 1
[4,4,2,2,2,1,1] => 0000011 => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[4,3,3,3,3] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,3,3,3,2,1] => 011101 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[4,3,3,2,2,2] => 011000 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,2,2,2,1] => 0100001 => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3
[4,2,2,2,2,2,2] => 0000000 => [8] => ([],8) => 1
[3,3,3,3,3,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[3,3,3,3,2,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[3,3,3,2,2,2,1] => 1110001 => [1,1,1,4,1] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5
[3,3,2,2,2,2,2] => 1100000 => [1,1,6] => ([(5,6),(5,7),(6,7)],8) => 3
[17] => 1 => [1,1] => ([(0,1)],2) => 2
[16,1] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[15,2] => 10 => [1,2] => ([(1,2)],3) => 2
[15,1,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[14,3] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[14,2,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[14,1,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[13,4] => 10 => [1,2] => ([(1,2)],3) => 2
[13,3,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[13,2,2] => 100 => [1,3] => ([(2,3)],4) => 2
[13,2,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[13,1,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[12,5] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[12,4,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[12,3,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[12,3,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[12,2,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[12,2,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[12,1,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[11,6] => 10 => [1,2] => ([(1,2)],3) => 2
[11,5,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[11,4,2] => 100 => [1,3] => ([(2,3)],4) => 2
[11,4,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[11,3,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[11,3,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[11,3,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[11,2,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[11,2,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[11,2,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[10,7] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[10,6,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[10,5,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[10,5,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[10,4,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[10,4,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[10,4,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[10,3,3,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[10,3,2,2] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[10,3,2,1,1] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[10,3,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[10,2,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[10,2,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[9,8] => 10 => [1,2] => ([(1,2)],3) => 2
[9,7,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[9,6,2] => 100 => [1,3] => ([(2,3)],4) => 2
[9,6,1,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[9,5,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[9,5,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[9,5,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[9,4,4] => 100 => [1,3] => ([(2,3)],4) => 2
[9,4,3,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[9,4,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[9,4,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[9,4,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[9,3,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[9,3,3,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[9,3,2,2,1] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[9,3,2,1,1,1] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[9,2,2,2,2] => 10000 => [1,5] => ([(4,5)],6) => 2
[9,2,2,2,1,1] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[8,8,1] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,7,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[8,7,1,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[8,6,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[8,6,2,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[8,6,1,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[8,5,4] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[8,5,3,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[8,5,2,2] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[8,5,2,1,1] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[8,5,1,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[8,4,4,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[8,4,3,2] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[8,4,3,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[8,4,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[8,4,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[8,3,3,3] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[8,3,3,2,1] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[8,3,3,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[8,3,2,2,2] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[8,3,2,2,1,1] => 010011 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[8,2,2,2,2,1] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[8,2,2,2,1,1,1] => 0000111 => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[7,7,3] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[7,7,2,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,7,1,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[7,6,4] => 100 => [1,3] => ([(2,3)],4) => 2
[7,6,3,1] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,6,2,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[7,6,2,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[7,6,1,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[7,5,5] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[7,5,4,1] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,5,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,5,3,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[7,5,2,2,1] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[7,5,2,1,1,1] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[7,4,4,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[7,4,4,1,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[7,4,3,3] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[7,4,3,2,1] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[7,4,3,1,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[7,4,2,2,2] => 10000 => [1,5] => ([(4,5)],6) => 2
[7,4,2,2,1,1] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,3,3,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[7,3,3,2,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[7,3,3,2,1,1] => 111011 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[7,3,2,2,2,1] => 110001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,2,2,2,2] => 100000 => [1,6] => ([(5,6)],7) => 2
[7,2,2,2,2,1,1] => 1000011 => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[6,6,5] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[6,6,4,1] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[6,6,3,2] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[6,6,3,1,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,6,2,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,6,2,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,5,5,1] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[6,5,4,2] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[6,5,4,1,1] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,5,3,3] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[6,5,3,2,1] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,5,3,1,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[6,5,2,2,2] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[6,5,2,2,1,1] => 010011 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,4,3] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[6,4,4,2,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,4,4,1,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,3,1] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,3,2,2] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,4,3,2,1,1] => 001011 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,2,2,1] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[6,4,2,2,1,1,1] => 0000111 => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[6,3,3,3,2] => 01110 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,3,3,1,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[6,3,3,2,2,1] => 011001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,2,2,2] => 010000 => [2,5] => ([(4,6),(5,6)],7) => 2
[6,3,2,2,2,1,1] => 0100011 => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[6,2,2,2,2,2,1] => 0000001 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,5,5,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,5,5,1,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,5,4,3] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,5,4,2,1] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,5,4,1,1,1] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,5,3,3,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,5,3,2,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,5,3,2,1,1] => 111011 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,5,2,2,2,1] => 110001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,4,4] => 1000 => [1,4] => ([(3,4)],5) => 2
[5,4,4,3,1] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,4,2,2] => 10000 => [1,5] => ([(4,5)],6) => 2
[5,4,4,2,1,1] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,3,2] => 10110 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,3,3,1,1] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,4,3,2,2,1] => 101001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,2,2,2] => 100000 => [1,6] => ([(5,6)],7) => 2
[5,4,2,2,2,1,1] => 1000011 => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[5,3,3,3,3] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,3,3,3,2,1] => 111101 => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[5,3,3,2,2,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,2,2,2,1] => 1100001 => [1,1,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[5,2,2,2,2,2,2] => 1000000 => [1,7] => ([(6,7)],8) => 2
[4,4,4,4,1] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,4,4,3,2] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,4,4,3,1,1] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,4,4,2,2,1] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,4,4,2,1,1,1] => 0000111 => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[4,4,3,3,3] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,4,3,3,2,1] => 001101 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,4,3,2,2,2] => 001000 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2
[4,4,3,2,2,1,1] => 0010011 => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[4,4,2,2,2,2,1] => 0000001 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,3,3,3,1] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[4,3,3,3,2,2] => 011100 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,3,2,2,2,1] => 0110001 => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
[4,3,2,2,2,2,2] => 0100000 => [2,6] => ([(5,7),(6,7)],8) => 2
[3,3,3,3,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[3,3,3,2,2,2,2] => 1110000 => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,1 2,0,1 2,0,2,0,1 4,0,2,0,1 3,0,5,0,2,0,1
$F_{1} = q^{2}$
$F_{2} = q + q^{3}$
$F_{3} = 2\ q^{2} + q^{4}$
$F_{4} = 2\ q + 2\ q^{3} + q^{5}$
$F_{5} = 4\ q^{2} + 2\ q^{4} + q^{6}$
$F_{6} = 3\ q + 5\ q^{3} + 2\ q^{5} + q^{7}$
Description
The achromatic number of a graph.
This is the maximal number of colours of a proper colouring, such that for any pair of colours there are two adjacent vertices with these colours.
This is the maximal number of colours of a proper colouring, such that for any pair of colours there are two adjacent vertices with these colours.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
odd parts
Description
Return the binary word indicating which parts of the partition are odd.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
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