Characterization of jacobian Newton polygons of plane branches and new   criteria of irreducibility
  In this paper we characterize, in two different ways, the Newton polygons which are jacobian Newton polygons of a branch. These characterizations give in particular combinatorial criteria of irreducibility for complex series in two variables and necessary conditions which a complex curve has to satisfy in order to be the discriminant of a complex plane branch. 
Evelia R. Garc\'ia Barroso and Janusz Gwo\'zdziewicz