The Lagrange Inversion Formula and Divisibility Properties
Washington, DC 20059
Wilf stated that the Lagrange inversion formula (LIF) is a remarkable tool for
solving certain kinds of functional equations, and at its best it can give
explicit formulas where other approaches run into stone walls. Here we
present the LIF combinatorially in the form of lattice paths,
and apply it to the
divisibility property of the coefficients of a formal power series expansion.
For the LIF, the coefficients are in a commutative ring with identity.
As for divisibility, we require the coefficients to be in a principal ideal
Full version: pdf,
Received November 19 2006;
revised version received July 26 2007.
Published in Journal of Integer Sequences, August 2 2007.
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