有限词中散列回文的计数
Counting scattered palindromes in a finite word
摘要：
我们研究有限词中分散的回文子词。我们首先用最少数量的分散回文子词来表征单词。然后，我们给出了一个上限的回文子字在一个字的长度$n$的斐波那契数$F_n$方面的回文子字的总数证明，最多$F_n$新的分散回文子字可以创建一个字母的长度$n-1$的字的串联。我们提出了一个猜想的最大数量分散回文子字的长度为$n$与$q$不同的字母。我们支持的猜想，显示其有效性的话，$q\geq \frac{n}{2}$。
英文摘要：
We investigate the scattered palindromic subwords in a finite word. We start by characterizing the words with the least number of scattered palindromic subwords. Then, we give an upper bound for the total number of palindromic subwords in a word of length $n$ in terms of Fibonacci number $F_n$ by proving that at most $F_n$ new scattered palindromic subwords can be created on the concatenation of a letter to a word of length $n-1$. We propose a conjecture on the maximum number of scattered palindromic subwords in a word of length $n$ with $q$ distinct letters. We support the conjecture by showing its validity for words where $q\geq \frac{n}{2}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
