A \emph{palindrome} is a word that reads the same forwards and backwards. A \emph{block palindrome factorization} (or \emph{BP-factorization}) is a factorization of a word into blocks that becomes palindrome if each identical block is replaced by a distinct symbol. We call the number of blocks in a BP-factorization the \emph{width} of the BP-factorization. The \emph{largest BP-factorization} of a word $w$ is the BP-factorization of $w$ with the maximum width. We study words with certain BP-factorizations. First, we give a recurrence for the number of length-$n$ words with largest BP-factorization of width $t$. Second, we show that the expected width of the largest BP-factorization of a word tends to a constant. Third, we give some results on another extremal variation of BP-factorization, the \emph{smallest BP-factorization}. A \emph{border} of a word $w$ is a non-empty word that is both a proper prefix and suffix of $w$. Finally, we conclude by showing a connection between words with a unique border and words whose smallest and largest BP-factorizations coincide.

翻译：\ emph{ palindrome} 是一个可以读出相同前向和后向的单词。 $$( emph{ block) balintrodromization} (或 emph{ BBP- facilization} ) 是将单词转换成区块的系数, 如果每个相同区块都替换为不同的符号, 则该区块会变成巴林Drome 。 我们将BP- facilization 中的区块数称为 BP- contalization 。 一个单词的最大 BP{ bP- controduction 的预期宽度会保持不变 。 第三个, 我们给出了BP- droupalization $ 和 $ xmphxlest B- florminal 之间的另一极端变数, 和 $ B- bxxxxxxxx 之间最后显示一个不完全的字链接。</s>