The Lyndon factorization of a word has been largely studied and recently variants of it have been introduced and investigated with different motivations. In particular, the canonical inverse Lyndon factorization $\mathrm{ICFL}(w)$ of a word w, introduced in [1], maintains the main properties of the Lyndon factorization since it can be computed in linear time and it is uniquely determined. In this paper we investigate new properties of this factorization with the aim of exploring their use in some classical queries on w.

The main property we prove is related to a classical query on words. We prove that there are relations between the length of the longest common prefix (or longest common extension) $\mathrm{lcp}(x,y)$ of two different suffixes $x,y$ of a word w and the maximum length $\mathcal{M}$ of two consecutive factors of $\mathrm{ICFL}(w)$. More precisely, $\mathcal{M}$ is an upper bound on the length of $\mathrm{lcp}(x,y)$. A main tool used in the proof of the above result is a property that we state for factors $m_i$ with nonempty borders in $\mathrm{ICFL}(w)$: a nonempty border of $m_i$ cannot be a prefix of the next factor $m_{i+1}$.

Another interesting result relates sorting of global suffixes, i.e., suffixes of a word w, and sorting of local suffixes, i.e., suffixes of products of factors in $\mathrm{ICFL}(w)$. This is the counterpart for $\mathrm{ICFL}(w)$ of the compatibility property, proved in [2], [3] for the Lyndon factorization. Roughly, the compatibility property allows us to extend the mutual order between suffixes of products of the (inverse) Lyndon factors to the suffixes of the whole word.

The last property we prove focuses on the Lyndon factorizations of a word and its factors. It suggests that the Lyndon factorizations of two words sharing a common overlap could be used to capture the common overlap of these two words.

单词的Lyndon因式分解已得到广泛研究，最近又以不同的动机对它的变体进行了介绍和研究。尤其是正则逆Lyndon分解$\mathrm{国际足球联合会}（w）$在[1]中引入的单词w的词素保持Lyndon因式分解的主要属性，因为它可以在线性时间内计算并且可以唯一确定。在本文中，我们研究此分解的新属性，以探索它们在w的一些经典查询中的使用。

我们证明的主要属性与单词的经典查询有关。我们证明最长公共前缀（或最长公共扩展名）的长度之间存在关系$\mathrm{液晶显示器}（X，ÿ）$ 两个不同的后缀 $X，ÿ$一个字的瓦特和最大长度$\mathcal{中号}$ 两个连续因素的 $\mathrm{国际足球联合会}（w）$。更确切地说，$\mathcal{中号}$ 是长度的上限 $\mathrm{液晶显示器}（X，ÿ）$。以上结果证明中使用的主要工具是我们针对因素陈述的属性${米}_{\mathrm{一世}}$ 带有非空边界 $\mathrm{国际足球联合会}（w）$：的非空边界 ${米}_{\mathrm{一世}}$ 不能是下一个因素的前缀 ${米}_{\mathrm{一世}+\mathrm{1个}}$。

另一个有趣的结果涉及全局后缀（即单词w的后缀）的排序和局部后缀（即因子in的乘积的后缀）的排序$\mathrm{国际足球联合会}（w）$。这是对应的$\mathrm{国际足球联合会}（w）$的兼容性属性，在Lyndon因式分解中在[2]，[3]中得到了证明。粗略地讲，兼容性属性使我们能够将（逆）Lyndon乘积的后缀之间的相互顺序扩展到整个单词的后缀。

我们证明的最后一个属性集中在单词及其因素的Lyndon因式分解上。这表明可以使用共享共同重叠的两个单词的Lyndon分解来捕获这两个单词的共同重叠。