弧交叉变化下的可达性
Reachability under arc crossing changes
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中文总结 AI 辅助
本文改进了Cericola关于纽结图可通过弧交叉变换为升式未纽结图的结果，明确了R₁-约化经典纽结影子上交叉数大于3的图的可达性关系，通过标记高斯字的局部五出现条件刻画源图。
中文摘要 AI 辅助
Cericola证明，每个纽结图都可通过弧交叉变换为升式未纽结图。本文针对固定的R₁-约化经典纽结影子上、交叉数大于3的所有图，对该结果进行了改进：除至多2个源图外，任意两个具有相同状态奇偶性的图相互可达；每个源图可达其奇偶类下的所有非源图，但无法被其他图到达；标记高斯字上的局部五出现条件可刻画这些源图，进而确定完整的有向可达性关系。
英文摘要
Cericola proved that every knot diagram can be transformed into an ascending unknot diagram by arc crossing changes. We refine this result for all diagrams on a fixed R1-reduced classical knot shadow with more than three crossings. Apart from at most two source diagrams, any two diagrams of the same state parity are mutually reachable. Each source diagram reaches every non-source diagram of its parity but cannot be reached from another diagram. A local five-occurrence condition on the marked Gauss word characterizes the sources and thereby determines the full directed reachability relation.
