An equivalence for irreducible parametrization and its applications to the direct proof of an equivalence of the Puiseux pairs and the multiplicity sequences for irreducible curves (Q1769395)

The main result proved in this paper is the following well-known theorem about a singular point on a branch of a plane algebraic curve defined over the complex numbers: If two plane curves, both analytically irreducible at a point \(O,\) have the same characteristic pairs (relative to possibly different parametrizations), then they have the same multplicity sequence (for points infinitely near \(O\)) and conversely. The reviewer had difficulty in trying to find anything new in the author's approach. Strangely, the author states in the abstract that the aim of the paper is to (re?) prove the above theorem without making use of the topological equivalence of the singularities having the same characteristic pairs. But the well known proofs (referred to in the article) only use algebraic properties of quadratic transformations along with inversion and invariance of characteristic pairs.