A factorization for formal laurent series and lattice path enumeration

Abstract

If f = Σn=-∞∞ antn is a formal Laurent series with certain restrictions on the an, then f = f-f0f+, where f- contains only negative powers of t, f+ contains only positive powers of t, and f0 is independent of t. Applications include Lagrange's formula for series reversion, the problem of counting lattice paths below a diagonal, and a theorem of Furstenberg that the diagonal of a rational power series in two variables is algebraic. © 1980.