Reversion of power series and the extended Raney coefficients

DOI10.1090/S0002-9947-97-01781-9zbMath0868.13019OpenAlexW1508570312MaRDI QIDQ4336539

Stuart Sui-Sheng Wang, Wright, David, Charles Ching-An Cheng, Jacob Towber, James H. McKay

Publication date: 13 May 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01781-9

zbMATH Keywords

Jacobian conjectureLaurent seriesformal power seriesRaney coefficientscolored treescolored forestsdiagonal reversiondirect reversionJacobi's residue formulareversion of a system of power series

Mathematics Subject Classification ID

Trees (05C05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Computational aspects and applications of commutative rings (13P99) Power series, series of functions of several complex variables (32A05) Formal power series rings (13F25)

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D-log and formal flow for analytic isomorphisms of n-space, Étale exoticity of the Pinchuk surface, Bounded Factorization and the Ascending Chain Condition on Principal Ideals in Generalized Power Series Rings, Changes of Parameters for Generalized Power Series, Two applications of analytic functors, A counting formula for labeled, rooted forests, Faà di Bruno's formula and inversion of power series, Laplace's method on a computer algebra system with an application to the real valued modified Bessel functions, Generalized power series with a limited number of factorizations, A residue theorem for Malcev-Neumann series.

Cites Work

• The tree formulas for reversion of power series
• A Jacobian criterion for separability
• Incidence algebra antipodes and Lagrange inversion in one and several variables
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
• Functional Composition Patterns and Power Series Reversion
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