Combinatorial mathematics can be generally described as: combination of mathematical research is the existence of discrete structures, counting, analysis and optimization problems, such as the one subject (see the literature [3]). Counting is the combination of mathematics in one of the main content, and generating function is an important tool for counting, therefore, the mother of mathematical functions in the portfolio has an important position is to solve the problem of combination of powerful tools. This paper describes the generating function and index-generating function in combination count, with counts, recursive relationship, combined identity and integral split in some applications.
Key words: generating function, the index-generating function, the combination of counting, with counting, sorting, combined
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