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ISSN 1088-6850(e) ISSN 0002-9947(p)

D-log and formal flow for analytic isomorphisms of n-space

Author(s): David Wright; Wenhua Zhao
Journal: Trans. Amer. Math. Soc. 355 (2003), 3117-3141.
MSC (2000): Primary 14R10, 11B68; Secondary 14R15, 05C05
Posted: April 14, 2003
MathSciNet review: 1974678
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Abstract: Given a formal map $F=(F_1,\ldots,F_n)$ of the form $z+\text{higher-order}$ terms, we give tree expansion formulas and associated algorithms for the D-Log of and the formal flow . The coefficients that appear in these formulas can be viewed as certain generalizations of the Bernoulli numbers and the Bernoulli polynomials. Moreover, the coefficient polynomials in the formal flow formula coincide with the strict order polynomials in combinatorics for the partially ordered sets induced by trees. Applications of these formulas to the Jacobian Conjecture are discussed.

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