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

Authors:
David Wright and Wenhua Zhao

Journal:
Trans. Amer. Math. Soc. **355** (2003), 3117-3141

MSC (2000):
Primary 14R10, 11B68; Secondary 14R15, 05C05

DOI:
https://doi.org/10.1090/S0002-9947-03-03295-1

Published electronically:
April 14, 2003

MathSciNet review:
1974678

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a formal map of the form 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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Additional Information

**David Wright**

Affiliation:
Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130-4899

Email:
wright@einstein.wustl.edu

**Wenhua Zhao**

Affiliation:
Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130-4899

Email:
zhao@math.wustl.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03295-1

Keywords:
D-log,
formal flow of automorphisms,
rooted trees,
order polynomials,
Bernoulli numbers and polynomials

Received by editor(s):
June 5, 2002

Received by editor(s) in revised form:
January 3, 2003

Published electronically:
April 14, 2003

Article copyright:
© Copyright 2003
American Mathematical Society