组合Gray码——一项更新的综述
Combinatorial Gray codes-an updated survey
AI总结：
本文综述了组合Gray码研究的最新进展，更新了Savage的经典综述，涵盖多种组合对象的Gray码列表，并强调其与图论、代数等领域的联系，提出未来挑战性问题以激发新研究。
摘要：
组合Gray码是针对一类对象的列表，其中包含该类的每个对象恰好一次，使得列表中任意两个连续对象仅相差一个“微小变化”。许多不同的组合对象都有这种列表，包括位串、组合、排列、划分、三角剖分，以及相对于固定图定义的对象，如生成树、完美匹配或顶点着色。本综述提供了组合Gray码研究最新进展的全面图景。特别地，它更新了Savage的有影响力的综述[C. D. Savage. A survey of combinatorial Gray codes. SIAM Rev., 39(4):605--629, 1997.]，纳入了许多更新的进展。我们还强调了与图论、代数、序论、几何和算法中密切相关问题的联系，从而将这一研究领域嵌入更广阔的背景中。最后，我们收集并提出了一些具有挑战性的研究问题，从而激发新的研究努力。
英文摘要：
A combinatorial Gray code for a class of objects is a listing that contains each object from the class exactly once such that any two consecutive objects in the list differ only by a `small change'. Such listings are known for many different combinatorial objects, including bitstrings, combinations, permutations, partitions, triangulations, but also for objects defined with respect to a fixed graph, such as spanning trees, perfect matchings or vertex colorings. This survey provides a comprehensive picture of the state-of-the-art of the research on combinatorial Gray codes. In particular, it gives an update on Savage's influential survey [C. D. Savage. A survey of combinatorial Gray codes. SIAM Rev., 39(4):605--629, 1997.], incorporating many more recent developments. We also emphasize the connections to closely related problems in graph theory, algebra, order theory, geometry and algorithms, which embeds this research area into a broader context. Lastly, we collect and propose a number of challenging research problems, thus stimulating new research endeavors.
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