A combinatorial proof of the multivariable lagrange inversion formula

A Physicist’s Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using the techniques of quantum field theory.

The Lagrange Inversion Formula and Divisibility Properties

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 Planar Tree Lagrange Inversion Formula

A One-parameter Deformation of the Noncommutative Lagrange Inversion Formula

We give a one-parameter deformation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder-Frabetti-Krattenthaler for the antipode of the noncommutative Faá di Bruno algebra. Namely, we obtain a closed formula for the antipode of the one-parameter deformation of this Hopf algebra discovered by Foissy.

A short proof of the Lagrange-Good formula

Since Good’s paper [5j appeared in 1960, :i lot of other works have been published on this theme. Good’s proof of his theorem being analytical, <:he later authors considered Lagrange inversion within the theory of formal power series. The first attempt for a purely combinatorial proof was made by Chottin [ 1 j, who treated a special case of the two dimensional formula. Tutte gave an extensive d...