中文摘要：

本文研究了两分支的自相似集的问隙序列与维数之间的关系．Besicovitch和Taylor证明了R上的白相似集的维数由它的间隙序列所确定（见文献[1]）．利用生成函数的方法，证明了对一类两分支的白相似集，其间隙序列由维数所确定；并且猜测这一结论对一股的自相似集均成立．

英文摘要：

In this paper, we study the relation between the dimension and gap sequences with two branches of self-similar sets. For self-similar sets in I, Besicovitch and Taylor proved that the dimension is determined by the gap sequences （see [1]）. In this paper, using generating function method, we show that the inverse is also true for a class of self-similar sets with two branches, and we guess the inverse is true in general. It suggests that for self-similar sets, gap sequence is no better than dimension as Lipschitz invariant.