Partitions enumerated by

Partitions enumerated by

Partitions enumerated by

0

1

Empty partition

1

Empty partition

1

Empty partition

1

1

1₁

0

-

1

1

2

1

2₂

1

2

2

2, 1 + 1

3

0

-

1

3

2

2 + 1, 1 + 1 + 1

4

1

3₁ + 1₁

1

2 + 2

4

4, 2 + 2, 2 + 1 + 1,

1 + 1 + 1 + 1

5

2

5₁, 4₂ + 1₁

1

3 + 2

5

5, 4 + 1, 2 + 2 + 1,

2 + 1 + 1 + 1,

1 + 1 + 1 + 1 + 1

6

1

6₂

3

6, 3 + 3, 2 + 2 + 2

7

5 + 1, 4 + 2, 4 + 1 + 1,

2 + 2 + 2, 2 + 2 + 1 + 1,

2 + 1 + 1 + 1 + 1

1 + 1 + 1 + 1 + 1 + 1

7

1

5₁ + 2₂

1

3 + 2 + 2

9

7, 5 + 2, 5 + 1 + 1,

4 + 2 + 1, 4 + 1 + 1 + 1,

2 + 2 + 2 + 1,

2 + 2 + 1 + 1 + 1,

2 + 1 + 1 + 1 + 1 + 1,

1 + 1 + 1 + 1 + 1 + 1 + 1