生成函数的应用

Application of Generating Function

从六个方面介绍了生成函数的应用,重点介绍其求解递归公式的通项、在组合计数上的应用和证明恒等式,另外还介绍了求平均值、证明单峰性、证明同余三个方面的应用.

This paper introduces the applications of generating function from six aspects,focusing on the solutions of the general terms about the recursive formulas,the applications of combinatorial enumeration and the proofs of identical equations.It also introduces the other three applications in the average value,unimodality-proving and congruence-proving.