A ONE-PARAMETER DEFORMATION OF THE NONCOMMUTATIVE 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.

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 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.

A Multivariate Lagrange Inversion Formula for Asymptotic Calculations

The determinant that is present in traditional formulations of multivariate Lagrange inversion causes di culties when one attempts (d+1) 1 terms in contrast to the d! terms of the determinantal form. Thus it is likely to prove useful only for asymptotic purposes. 1991 AMS Classi cation Number. Primary: 05A15 Secondary: 05C05, 40E99 the electronic journal of combinatorics 5 (1998), #Rxx 2