Merino-Mička-Mütze 对 Knuth 组合生成问题方法的另一种形式
An alternate form of Merino-Mička-Mütze's approach to a combinatorial generation problem of Knuth
AI总结：
本文提出 Merino-Mička-Mütze 解答 Knuth 组合生成问题的另一种形式，并用二面体商图与 Dyck 词的有根树排序统一表达生成 Hamilton 圈的周期路径。
摘要：
本综述提出了对 Merino-Mička-Mütze 关于 Knuth 组合生成问题解答的一种修改。由此得到的该解答的另一种形式与作者对中层图 Hamilton 圈存在性证明的重新解释相容。这种重新解释通过一个与每个中层图相关联的二面体商图给出。该商图的顶点表示 Dyck 词及其关联的有序树。这些 Dyck 词通过一棵有根树被线性排序，该有根树覆盖了它们所有的紧形式（即不可约形式），从而提供了一个通用的参考视角来表达和整合那些周期路径（或称为块），这些周期路径的拼接导致了由上述解答所产生的 Hamilton 圈。
英文摘要：
A modification of Merino-Mička-Mütze's solution to a combinatorial generation problem of Knuth is proposed in this survey. The resulting alternate form to such solution is compatible with a reinterpretation by the author of a proof of existence of Hamilton cycles in the middle-levels graphs. Such reinterpretation is given in terms of a dihedral quotient graph associated to each middle-levels graph. The vertices of such quotient graph represent Dyck words and their associated ordered trees. Those Dyck words are linearly ordered via a rooted tree that covers all their tight, or irreducible, forms, offering an universal reference point of view to express and integrate the periodic paths, or blocks, whose concatenation leads to Hamilton cycles resulting from the said solution.
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