On the Euler's Partition Theorem

Sa？etak In this paper, we present the Euler's partition theorem, which states that for every natural number the number of odd partitions is equal to the number of strict partitions. First, we prove this theorem bijectively and then using generating functions. We present two Sylvester's bijections which, besides proving Euler's theorem, also give a few other refinements. Fine's theorem is illustrated by using Dyson's bijection iteratively on concrete examples