Absolute irreducibility of polynomials via newton polytopes

A multivariable polynomial is associated with a polytope, called its Newton polytope. A polynomial is absolutely irreducible if its Newton polytope is indecomposable in the sense of Minkowski sum of polytopes. Two general con structions of indecomposable polytopes are given, and they give many simple irreducibility criteria including the well-known Eisenstein criterion. Pol ynomials from these criteria are over any field and have the property of re maining absolutely irreducible when their coefficients are modified arbitra rily in the field. but keeping a certain collection of them nonzero. (C) 20 01 Academic Press