Abstract A word over an n -ary alphabet is called minimal-palindromic if it does not contain palindromic subwords whose length is greater than ⌈ | w | n ⌉ (note that each n -ary word must contain a palindromic subword of at least that length: for example, a subword consisting of a prevalent letter, which explains the term “minimal-palindromic”). The MP-ratio of a given word w is defined as the quotient | r w s | | w | , where r and s are (possibly empty) words such that the word r w s is minimal-palindromic and that the length | r | + | s | is minimal possible. We show that the MP-ratio is well-defined in the ternary case (that is, that such words r and s always exist), as well as that it is bounded from above by the constant 6 and that 6 is the best possible upper bound.

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关于高度回文词：三元情况

摘要 在 n 元字母表上的单词如果不包含长度大于 ⌈ | 的回文子词，则称为最小回文词。| | n ⌉（请注意，每个 n 元单词必须包含一个至少该长度的回文子词：例如，一个由流行字母组成的子词，这解释了术语“最小回文”）。给定单词 w 的 MP 比率定义为商 | rws | | | | ，其中 r 和 s 是（可能是空的）词，使得词 rws 是最小回文并且长度 | r | + | | 是最小的可能。我们表明 MP 比率在三元情况下是明确定义的（即，这样的词 r 和 s 总是存在），并且它从上面受到常数 6 的限制，并且 6 是可能的最佳上限边界。