Subset-lex：我们是否错过了一种顺序？
Subset-lex: did we miss an order?
AI总结：
本文推广了按 subset-lex 顺序生成集合子集的算法，为多重集子集、组合、划分及受限增长串等组合对象设计了通常无循环且高效的生成算法，并描述了对应的 Gray code。
摘要：
我们推广了一种著名算法，该算法用于按集合作为元素列表的字典顺序（subset-lex 顺序）生成集合的所有子集。我们获得了针对各种组合对象的算法，例如多重集的子集、表示为部分列表的组合与划分，以及某些受限增长串。这些算法通常是无循环的，且最多需要一个额外变量来计算下一个对象。即使非无循环时，算法的性能也极具竞争力。文中还描述了对应于 subset-lex 顺序的 Gray code 以及在此工作中发现的用于组合的 Gray code。
英文摘要：
We generalize a well-known algorithm for the generation of all subsets of a set in lexicographic order with respect to the sets as lists of elements (subset-lex order). We obtain algorithms for various combinatorial objects such as the subsets of a multiset, compositions and partitions represented as lists of parts, and for certain restricted growth strings. The algorithms are often loopless and require at most one extra variable for the computation of the next object. The performance of the algorithms is very competitive even when not loopless. A Gray code corresponding to the subset-lex order and a Gray code for compositions that was found during this work are described.
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。
