A Multivariate Lagrange Inversion Formula for Asymptotic Calculations

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

Multivariate Lagrange inversion formula and the cycle lemma

We give a multitype extension of the cycle lemma of (Dvoretzky and Motzkin 1947). This allows us to obtain a combinatorial proof of the multivariate Lagrange inversion formula that generalizes the celebrated proof of (Raney 1963) in the univariate case, and its extension in (Chottin 1981) to the two variable case. Until now, only the alternative approach of (Joyal 1981) and (Labelle 1981) via l...

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

Recent Results for the Q-lagrange Inversion Formula

A survey of the q-Lagrange inversion formula is given, including recent work of Garsia, Gessel, Hofbauer, Krattenthaler, Remmel, and Stanton. Some applications to identities of Rogers-Ramanujan type are stated.