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hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
dc.contributor.authorBOUSQUET-MÉLOU, Mireille
hal.structure.identifierThéorie des Nombres et Algorithmique Arithmétique [A2X]
dc.contributor.authorJEHANNE, Arnaud
dc.date.issued2006
dc.identifier.issn0095-8956
dc.description.abstractEnLet $F(t,u)\equiv F(u)$ be a formal power series in $t$ with polynomial coefficients in $u$. Let $F_1 , \ldots, F_k$ be $k$ formal power series in $t$, independent of $u$. Assume all these series are characterized by a polynomial equation $$ P(F(u), F_1, \ldots , F_k, t , u)=0. $$ We prove that, under a mild hypothesis on the form of this equation, these $(k+1)$ series are algebraic, and we give a strategy to compute a polynomial equation for each of them. This strategy generalizes the so-called kernel method, and quadratic method, which apply respectively to equations that are linear and quadratic in $F(u)$. Applications include the solution of numerous map enumeration problems, among which the hard-particle model on general planar maps.
dc.language.isoen
dc.publisherElsevier
dc.subject.engenerating functions
dc.subject.enenumeration
dc.subject.enkernel method
dc.subject.enplanar maps
dc.subject.enfunctional equations
dc.subject.enquadratic method
dc.title.enPolynomial equations with one catalytic variable, algebraic series, and map enumeration
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.identifier.arxivmath.CO/0504018
bordeaux.journalJournal of Combinatorial Theory, Series B
bordeaux.page623--672.
bordeaux.volume96
bordeaux.peerReviewedoui
hal.identifierhal-00004621
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00004621v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Combinatorial%20Theory,%20Series%20B&rft.date=2006&rft.volume=96&rft.spage=623--672.&rft.epage=623--672.&rft.eissn=0095-8956&rft.issn=0095-8956&rft.au=BOUSQUET-M%C3%89LOU,%20Mireille&JEHANNE,%20Arnaud&rft.genre=article


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