Symbolic method (combinatorics): Difference between revisions

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{{About|the method in analytic combinatorics|the method in invariant theory|Symbolic method}}

In [[combinatorics]], especially in analytic 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]]''.

Similar languages for specifying combinatorial classes and their generating functions are found in work by

Bender and Goldman,<ref>{{cite journal|last1=Bender|first1=E.A.|last2=Goldman|first2=J.R.|title=Enumerative uses of generating functions|journal=Indiana Univ. Math. J.|date=1971|volume=20|pages=753–764}}</ref> Foata and Schützenberger,<ref name="fs">{{cite journal|last1=Foata|first1=D.|last2=Schützenberger|first2=M.|title=Théorie géométrique des polynômes Eulériens|journal=Lectures Notes in Math.|date=1970|volume=138}}</ref> and Joyal.<ref>{{cite journal|last1=Joyal|first1=Andre|title=Une théorie combinatoire des séries formelles|journal=Adv. Math.|date=1981|volume=42|pages=1–82|ref=joy}}</ref>

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{{reflist}}

* François Bergeron, Gilbert Labelle, Pierre Leroux, ''Théorie des espèces et combinatoire des structures arborescentes'', LaCIM, Montréal (1994). English version: ''Combinatorial Species and Tree-like Structures'', Cambridge University Press (1998).

* Philippe Flajolet and Robert Sedgewick, ''[[Analytic Combinatorics]]'', Cambridge University Press (2009). (available online: http://algo.inria.fr/flajolet/Publications/book.pdf)

* Micha Hofri, ''Analysis of Algorithms: Computational Methods and Mathematical Tools'', Oxford University Press (1995).