Example. The partitions of 5 are:

5

4 1

3 2

3 1 1

2 2 1

2 1 1 1

1 1 1 1 1

The -ordered- partitions of 5 are:

5

4 1

1 4

3 2

2 3

3 1 1

1 3 1

1 1 3

2 2 1

2 1 2

1 2 2

2 1 1 1

1 2 1 1

1 1 2 1

1 1 1 2

1 1 1 1 1

Note:

1 ( of 1 ) = C(4,0)

4 ( of 2 ) = C(4,1)

6 ( of 3 ) = C(4,2)

4 ( of 4 ) = C(4,3)

1 ( of 5 ) = C(4,4)

The number of ordered partitions of n = 2^(n-1). In the case of 5: 2^4=16.

Try 3,4 or 6 as an ( interesting ) exercise.

2-2018 Teaching by misleading

2 months ago

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