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Enumerative Combinatorics, Second Edition by Richard P. Stanley

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4

Rational Generating Functions

4.1 Rational Power Series in One Variable

The theory of binomial posets developed in the previous chapter sheds considerable light on the “meaning” of generating functions and reduces certain types of enumerative problems to a routine computation. However, it does not seem worthwhile to attack more complicated problems from this point of view. The remainder of this book will for the most part be concerned with other techniques for obtaining and analyzing generating functions. We first consider the simplest general class of generating functions, namely, the rational generating functions. In this chapter we will concern ourselves primarily with rational generating functions in one variable; that is, generating functions ...

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