Generating functions, one of the most important tools in
enumerative combinatorics, are a bridge between discrete
mathematics and continuous analysis. Generating functions have
numerous applications in mathematics, especially in: Combinatorics;
Probability Theory; Statistics; Theory of Markov Chains; and Number
Theory. One of the most important and relevant recent applications
of combinatorics lies in the development of Internet search
engines, whose incredible capabilities dazzle even the
mathematically trained user.
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