Set partitions are arrangements of distinct objects into groups. The problem of listing all set partitions arises in a variety of settings, in particular in combinatorial optimization tasks. After a brief review, we give practical approximate formulas for determining the number of set partitions, both for small and large set sizes. Several algorithms for enumerating all set partitions are reviewed, and benchmarking tests were conducted. The algorithm of Djokic et al. is recommended for practical use.

翻译：集合划分是将不同对象分组排列的方法。列举所有集合划分的问题出现在多种场景中，特别是在组合优化任务中。在简要回顾后，我们给出了用于确定集合划分数量的实用近似公式，适用于小规模和大规模集合。本文回顾了多种枚举所有集合划分的算法，并进行了基准测试。推荐在实际应用中使用Djokic等人提出的算法。