Hello,

Have you shown that the number of self conjugate unrestricted partitions of n is equal to the number of partitions of n into distinct odd parts?

Thanks for your answers

Yes. If your definition of an "unrestricted" partition is simply a partition without any further constraint being given.

See the claim in the above link:

**Claim:** The number of self-conjugate partitions is the same as the number of partitions with distinct odd parts.

For instance, (5, 5, 4, 3, 2) |- n, where n=19, is a self-conjugate partition. It converts into the 9+7+3=19. Read the link I provided. It will give you some explanations graphically.

The link I provided only shows the sketch of the proof. I encourage you to make a full proof on your own by using the sketch of the proof in the link.