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首页> 外文期刊>Discrete Applied Mathematics >Counter-intuitive answers to some questions concerning minimal-palindromic extensions of binary words
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Counter-intuitive answers to some questions concerning minimal-palindromic extensions of binary words

机译：对与二进制单词的最小回文扩展有关的一些问题的反直觉答案

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In [. Holub, K. Saari, On highly palindromic words, Discrete Appl. Math. 157 (2009) 953959] the authors proposed to measure the degree of "palindromicity" of a binary word w by ratio |rws||w|, where the word rws is minimal-palindromicthat is, does not contain palindromic subwords of length greater than |w|2?and the length |r|+|s| is as small as possible. It was asked whether the words of a given length n which reach the maximal possible ratio |rws||w| among the words of length n are always palindromes. It was further asked whether it can be assumed, w.l.o.g., that r and s are of form 0~* or 1~*, or at least 0 ~*1~* or 1~*0~*. We negatively answer these questions, and also one further question of a similar kind.
机译：在[。 Holub，K。Saari，关于回文率高的单词，Discrete Appl。数学。 157（2009）953959]作者提议通过比率| rws || w |来测量二元词w的“回文性”程度，其中rws是最小回文，即不包含长度大于的回文子词。 | w | 2？和长度| r | + | s |尽可能小。询问给定长度n的单词是否达到最大可能比率| rws || w |。在长度为n的单词中，总是回文。进一步询问是否可以假设，例如，r和s的形式为0〜*或1〜*，或至少为0〜* 1〜*或1〜* 0〜*。我们会否定地回答这些问题，并且还会再回答类似的问题。

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