Lyndon Words, the Three Squares Lemma, and Primitive Squares
Lyndon Words, the Three Squares Lemma, and Primitive Squares
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林登词、三平方引理和原平方
DOI：
10.1007/978-3-030-59212-7_19
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Yuto Nakashima
中科院分区：
文献类型：
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作者：
Hideo Bannai;Takuya Mieno;Yuto Nakashima
我们重新审视所谓的“三个正方形引理”的Crochemore和Rytter [Eschermica 1995]，并使用参数的基础上林登的话，得出一个更一般的变种，认为三个重叠的广场不一定有一个共同的前缀。我们还给出了一个改进的上限ofon的最大数量（出现）的rectively扎根广场在一个字符串的长度n，也使用参数的基础上林登的话。据我们所知，唯一已知的上限是，其中是黄金比例，由Fraenkel和Simpson [TCS 1999]通过三平方引理获得。
We revisit the so-called “Three Squares Lemma” by Crochemore and Rytter [Algorithmica 1995] and, using arguments based on Lyndon words, derive a more general variant which considers three overlapping squares which do not necessarily share a common prefix. We also give an improved upper bound ofon the maximum number of (occurrences of) primitively rooted squares in a string of lengthn, also using arguments based on Lyndon words. To the best of our knowledge, the only known upper bound was, whereis the golden ratio, reported by Fraenkel and Simpson [TCS 1999] obtained via the Three Squares Lemma.