Symbolic method (combinatorics): Difference between revisions

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In mathematics, the '''symbolic method''' is onea oftechnique the many techniques offor [[enumerative combinatorics|counting combinatorial objects]]. It uses the internal structure of the objects to derive formulas for their [[generating function]]s and then complex analysis techniques to get asymptotics. This particularThe theorymethod wasis mostly developedassociated bywith [[Philippe Flajolet]]{{Citation needed|date=October 2015}},

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

Earlier contributors to the key ideas and techniques include [[Leonhard Euler]], [[Arthur Cayley]], [[Srinivasa Ramanujan]], [[George Pólya]], and [[Donald Knuth]].

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 Schuetzenberger<ref name="fs">{{cite journal|last1=Foata|first1=D.|last2=Schuetzenberger|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>.

== Classes of combinatorial structures ==

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==References==

{{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)