An explicit formula for a bijective mapping from the set of distinct odd partitions into the set of self-conjugate partitions

In this paper, we give a full explicitly defined bijective function from the set of self-conjugate partitions to the set of partitions into distinct odd parts. The bijection between these two sets is well known since Euler. However, to our knowledge an explicit formula for such mapping from the set of distinct odd partitions into the set of selfconjugate partitions has not been given until now.