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：一个**回文**是指正向和反向读取相同的单词。**块回文分解**（或称为**BP-分解**）是将一个单词分解为若干块，若每个相同的块用不同的符号替换后，该分解序列成为回文。我们将BP-分解中的块数称为该BP-分解的**宽度**。单词$w$的**最大BP-分解**是指具有最大宽度的$w$的BP-分解。本文研究了具有特定BP-分解的单词。首先，我们给出了长度为$n$且最大BP-分解宽度为$t$的单词数量的递推关系。其次，我们证明了单词最大BP-分解的期望宽度趋于一个常数。第三，我们给出了关于BP-分解的另一种极值变体——**最小BP-分解**的一些结果。单词$w$的**边界**是指同时为$w$的真前缀和真后缀的非空单词。最后，我们通过展示具有唯一边界的单词与最小和最大BP-分解重合的单词之间的联系来结束本文。