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- W2045484872 abstract "Using his theory of combinatorial species, André Joyal proved in Advan. in Math. 42 (1981), 1–82 a combinatorial form of the classical multidimensional implicit function theorem. His theorem asserts the existence and (strong) unicity of species satisgying systems of combinatorial equations of a very general type. We present an explicit construction of these species by using a suitable combinatorial version of the Lie Series in the sense of 1., 2.. The approach constitutes a generalization of the method of “éclosions” (bloomings) which was used by the author in (J. Combin. Theory Ser. A 39, No. 1 (1985), 52–82), to study multidimensional power series reversion. Remarks concerning the applicability of the method to solve certain combinatorial differential equations are also made at the end of the work." @default.
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- W2045484872 date "1985-11-01" @default.
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- W2045484872 title "Une combinatoire sous-jacente au théorème des fonctions implicites" @default.
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- W2045484872 doi "https://doi.org/10.1016/0097-3165(85)90097-4" @default.
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