Multivariate Lagrange Inversion

A new formulation of Lagrange inversion for several variables will be described which does not involve a determinant. This formulation is convenient for the asymptotic investigation of numbers defined by Lagrange inversion. Examples of tree problems where the number of vertices of degree $k$ are counted and where vertices are 2-coloured will be given. Noncrossing partitions give another example and the Meir-Moon formula for powers of an inversion is a special case.