Journal of Integer Sequences, Vol. 10 (2007), Article 07.7.8

The Lagrange Inversion Formula and Divisibility Properties

Wen-jin Woan
Howard University
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 domain.

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Received November 19 2006; revised version received July 26 2007. Published in Journal of Integer Sequences, August 2 2007.

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