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In [[combinatorics]], the '''symbolic method''' is a technique for [[enumerative combinatorics|counting combinatorial objects]]. It uses the internal structure of the objects to derive formulas for their [[generating function]]s. The method is mostly associated with [[Philippe Flajolet]] and is detailed in Part A of his book with [[Robert Sedgewick (computer scientist)|Robert Sedgewick]], ''[[Analytic Combinatorics]]'', while the rest of the book explains how to use complex analysis in order to get asymptotic and probabilistic results on the corresponding generating functions.
During two centuries, generating functions were popping up via the corresponding recurrences on their coefficients (as can be seen in the seminal works of [[Daniel Bernoulli|Bernoulli]]
[[Srinivasa Ramanujan|Ramanujan]], [[John Riordan (mathematician)|Riordan]], [[Donald Knuth|Knuth]], {{ill|Louis Comtet|fr|lt=Comtet}}, etc.).
It was then slowly realized that the generating functions were capturing many other facets of the initial discrete combinatorial objects, and that this could be done in a more direct formal way: The recursive nature of some combinatorial structures
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