  In this report, we summarize the set partition enumeration problems and
thoroughly explain the algorithms used to solve them. These algorithms iterate
through the partitions in lexicographic order and are easy to understand and
implement in modern high-level programming languages, without recursive
structures and jump logic. We show that they require linear space in respect to
the set cardinality and advance the enumeration in constant amortized time. The
methods discussed in this document are not novel. Our goal is to demonstrate
the process of enumerating set partitions and highlight the ideas behind it.
This work is an aid for learners approaching this enumeration problem and
programmers undertaking the task of implementing it.
