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 elaborate on 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.

翻译：组合格雷码是针对一类对象的一种列举方式，要求该类的每个对象恰好出现一次，且列表中任意两个相邻对象仅存在"微小差异"。这类列举已广泛应用于多种组合对象，包括比特串、组合、排列、划分、三角剖分，以及基于固定图定义的对象（如生成树、完美匹配或顶点染色）。本综述全面描绘了组合格雷码研究的最新进展，特别更新了Savage的经典综述[C. D. Savage. A survey of combinatorial Gray codes. SIAM Rev., 39(4):605-629, 1997.]，整合了后续大量新成果。我们同时阐述了该领域与图论、代数、序理论、几何及算法中相关问题的深刻联系，从而将其置于更广阔的学术框架中。最后，我们系统整理并提出若干具有挑战性的研究问题，以期推动新的探索方向。