生成所有分区：两种编码的比较
Generating All Partitions: A Comparison Of Two Encodings
摘要：
为了系统生成的目的，可将递归分区编码为升序或降序组成。有许多算法可以生成所有的降序成分，但以前没有一个算法可以生成所有的升序成分。我们开发了三种新的算法来生成所有的上升组成，并比较这些下降组成生成器从文献中。我们分析了新的算法，并提供了新的和更精确的分析下降组成发电机。在每种情况下，升序合成生成算法比其降序合成对应算法有效得多。我们开发了一个新的配分函数p（n）的公式，作为我们的字典顺序规则的分析上升组成的一部分。
英文摘要：
Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate all ascending compositions. We develop three new algorithms to generate all ascending compositions and compare these with descending composition generators from the literature. We analyse the new algorithms and provide new and more precise analyses for the descending composition generators. In each case, the ascending composition generation algorithm is substantially more efficient than its descending composition counterpart. We develop a new formula for the partition function p(n) as part of our analysis of the lexicographic succession rule for ascending compositions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
