计算拼图组装的连通和非连通方式
Counting Connected and Disconnected Ways to Assemble a Jigsaw Puzzle
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中文总结 AI 辅助
研究如何计算拼图的组装方式，通过将拼图表示为图，利用图论结果枚举连通组装、从多不相连块开始的组装等三种策略，发现保持连通的组装序列远少于经过不相连中间阶段的序列。
中文摘要 AI 辅助
拼图可以通过多种不同方式组装。有些组装序列全程保持连通，而有些则先构建拼图的不同部分再拼接起来。将拼图表示为图后，这些组装序列就成为顶点排序，可利用图论结果进行计数。我们应用此框架枚举三种自然组装策略：连通组装、从多个不相连块开始的组装以及过程中可能开始新的不相连部分的组装。结果表明，即使对于中等大小的拼图，保持连通的组装序列数量也远少于经过不相连中间阶段的序列。
英文摘要
A jigsaw puzzle may be assembled in many different ways. Some assembly sequences remain connected throughout, while others temporarily build separate parts of the puzzle before joining them together. By representing the puzzle as a graph, these assembly sequences become vertex orderings that can be counted using recent results from graph theory. We apply this framework to enumerate three natural assembly strategies: connected assembly, assembly beginning from several disconnected pieces, and assembly in which new disconnected sections may be started during the process. The resulting counts reveal that, even for modest puzzle sizes, connectivity-preserving assembly sequences are greatly outnumbered by those that pass through disconnected intermediate stages.
