Lexicographic Enumeration of Set Partitions
Giorgos Stamatelatos, Pavlos S. Efraimidis

TL;DR
This paper reviews lexicographic algorithms for enumerating set partitions, emphasizing their simplicity, efficiency, and educational value, without introducing new methods.
Contribution
It provides a clear explanation and implementation guidance for existing set partition enumeration algorithms, focusing on their practical and educational aspects.
Findings
Algorithms operate in linear space
Enumeration advances in constant amortized time
Methods are easy to implement in high-level languages
Abstract
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics
