# partition and distinct summands wording problem

Could somebody kindly help me understand the definition of distinct summands in this context.

"...consider all partitions of 6 with distinct summands,

6 = 6,
6 = 5 + 1,
6 = 4 + 2,
6=3+2+1.

Here we have four equations, or four partitions, and this corresponds to the coefficient 4 in the term $$4x^6$$ of the expansion (7.1) (from the book"Maths of Choice).
"

The word distinct has popped up several times when working on partitions/summands word problems and I'm getting confused of it's definition here.

Does "distinct summands" means that the expression has only unique summands to be counted as one partition in this context. Example 3+2+1, all three summands are unique, hence, it's counted as 1 partition in the context of "distinct summands". And 3+1+1+1 shouldn't be counted as a partition with "distinct summands" since there is a repeat of 1s.

For reference, a none-conditional partition of 6 is as follow:
1 + 1 + 1 + 1 + 1 + 1
2+1+1+1+1

3+1+1+1
2+2+1+1

4+1+1
3+2+1
2+2+2

5+1
4+2
3+3

6

• Yes, "distinct summands" means that every number that appears in the partition appears only once. May 30, 2022 at 6:38