In this thesis, we will present bijective results related to integer partitions. Initially, the terminology and theoretical foundations of generating functions and partitions, necessary for understanding the work, are introduced. To understand the connection between bijective proof and generating functions, we will explore the decompositions of Young diagrams. We will present classic results from Euler’s pentagonal theorem, such as the recursive relationship for the number of partitions and Franklin’s involution. In the remainder of
the work, we address tools required to obtain two direct bijections of the recursive relationship. The first is the rank of partitions, which serves as a basis for Dyson’s mapping, with which we obtain an explicit direct bijection. The second tool is the principle of involution, which provides us with an iterative process to acquire another direct bijection.
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