1. ## Number Theory

An unrestricted partition (order does not count, equality of sizes is ok) partition is called self-conjugate if it is identical with its conjugate. E. g 8 = 4 + 2 + 1 + 1.

Show that the number of self conjugate unrestricted partitions of n is equal to the number of partitions of n into distinct odd parts

(optional) express this result as an identity of generating functions.

2. Originally Posted by Waikato
An unrestricted partition (order does not count, equality of sizes is ok) partition is called self-conjugate if it is identical with its conjugate. E. g 8 = 4 + 2 + 1 + 1.

Show that the number of self conjugate unrestricted partitions of n is equal to the number of partitions of n into distinct odd parts

(optional) express this result as an identity of generating functions.
A partition $\lambda$ is self-conjugate if $\lambda=\lambda'$ in terms of Ferrers diagram.

The bijection can be shown graphically. See wiki.

The generating function for this is $\prod_{\text{k=odd}}(1+x^k)=(1+x)(1+x^3)(1+x^5) \cdots$.

3. ## partition

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?

4. Originally Posted by Waikato
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?