On the Abhyankar-Moh inequality
  Abhyankar and Moh in their fundamental paper on the embeddings of the line in the plane proved an important inequality which can be stated in terms of the semigroup associated with the branch at infinity of a plane algebraic curve. In this note we study the semigroups of integers satisfying the Abhyankar-Moh inequality and give a simple proof of the Abhyankar-Moh embedding theorem. 
Roland D. Barrolleta, Evelia R. Garc\'ia Barroso, and Arkadiusz   P{\l}oski
math.AG