On the vertices of Newton polytopes associated with an automorphism of the ring of polynomials (Q1181436)

In the main result it is proved that if \(\sigma\) is an automorphism of the affine plane \(A_ n(k)\), with \(k\) a field of characteristic zero, then all the vertices of the Newton polytope \(N(\sigma x_ 1)\) are on the axis hyperplanes. This result extends a theorem of \textit{P. M. Cohn} about Newton polygons [Free rings and their relations. 2nd. ed. (London 1985; Zbl 0659.16001), pp. 341-352]. From the various techniques developed in the paper we notice the proof of the existence of a special family of independent leading forms.