中文摘要：

单边区间树可以通过对所给定的区间的多种分割方式进行构造，由此得到的区间树具有不同的性质．考察了分割中所产生的最大间隔问题，得到了不同分割方式下对应最大区间的极限分布所满足的形式不同的方程．通过递推，还得到了其中一些极限分布在某些小区间上的表达式．

英文摘要：

The one-sided interval trees can be generated by division a given interval in various ways. The corresponding interval trees have difference properties. The maximal gap in the corresponding interval was considered. Some functional equations for the asymptotic distributions of the length of the maximal gaps in difference ways of division were obtained. Using recurrence, the expressions of asymptotic distributions for several ways of division in some small intervals were also obtained.