指数生成函数在组合数学中有着重要的应用，本文给出了指数生成函数的概念，以及它们的若干性质，给出了在解决多重集的排列问题、组合恒等式的证明方面的具体应用，并着重阐述了其在允许重复排列问题上的具体运用-Index generating function in combinatorial mathematics has important applications, this paper, the concept of generating function index, as well as several of their nature, are given in solving the problem with multiple sets, proof of combinatorial identities of specific applications, and focus on elaborated in order to allow the issue of duplication of the concrete application of