论文标题
星状轴检测和分类
Star Anagram Detection and Classification
论文作者
论文摘要
星状镜头是一个单词字母的重新排列，可以产生另一个单词，没有字母保留其原始邻居。这些最大的浮标很少见，仅占英文的5.7％的字词。它们也可以描述为具有不同形式的单头多边形，包括同名恒星。我们开发了自动化方法，用于检测其他字符范围内的恒星，并根据其多边形旋转和反射对称性的多边形度对它们进行分类。接下来，我们探讨了星形词的几种属性，包括有关两个结果的证明，即有关完美的边缘长度，即最大对称性，恒星利用了与模块化算术和著名的中国剩余定理的令人惊讶的连接。最后，我们详尽地搜索了英语对星状hagrams，并提供了有关它们将其聚集成常见形状的数字结果以及几何值得注意的恒星的示例。
A star anagram is a rearrangement of the letters of one word to produce another word where no letter retains its original neighbors. These maximally shuffled anagrams are rare, comprising only about 5.7% of anagrams in English. They can also be depicted as unicursal polygons with varying forms, including the eponymous stars. We develop automated methods for detecting stars among other anagrams and for classifying them based on their polygon's degree of both rotational and reflective symmetry. Next, we explore several properties of star anagrams including proofs for two results about the edge lengths of perfect, i.e., maximally symmetric, stars leveraging perhaps surprising connections to modular arithmetic and the celebrated Chinese Remainder Theorem. Finally, we conduct an exhaustive search of English for star anagrams and provide numerical results about their clustering into common shapes along with examples of geometrically noteworthy stars.
