In a recent paper, Müllner and Ryzhikov posed a question about palindromic subwords of finite binary words which can be rephrased as follows: Given four equally long binary words $w_1,w_2,w_3,w_4$ of total length n, what is the size of a longest palindrome $p=q{q}^R$ such that (i) q is a subword of $w_1{w}_2$ and also of ${(w_3{w}_4)}^R$ or (ii) q is a subword of $w_2{w}_3$ and also of ${(w_4{w}_1)}^R$? Müllner and Ryzhikov conjectured that the answer is at least $n/2$. We disprove this conjecture, constructing sequences of words $w_1,w_2,w_3,w_4$ such that the longest palindromes have size $15n/32+o(n)$. Additionally, we show that the longest palindromes have size at least $3n/8$.

在最近的一篇论文中，Müllner 和 Ryzhikov 提出了一个关于有限二进制词的回文子词的问题，可以改写如下：给定四个等长的二进制词 ${瓦}_1,{瓦}_2,{瓦}_3,{瓦}_4$总长度为n，最长回文的大小是多少$磷=q{q}^{\mathrm{电阻}}$使得(i) q是${瓦}_1{瓦}_2$ 还有 ${({瓦}_3{瓦}_4)}^{\mathrm{电阻}}$或(ii) q是${瓦}_2{瓦}_3$ 还有 ${({瓦}_4{瓦}_1)}^{\mathrm{电阻}}$? Müllner 和 Ryzhikov 推测答案至少是$n/2$. 我们反驳这个猜想，构建单词序列${瓦}_1,{瓦}_2,{瓦}_3,{瓦}_4$ 这样最长的回文有大小 $15n/32+○(n)$. 此外，我们表明最长的回文至少有$3n/8$.