For any field F, there is a relation between the factorization of a polynomial f \in F[x_1,...,x_n] and the integral decomposition of the Newton polytope of f. We extended this result to polynomial rings R[x_1,...,x_n] where R is any ring containing some elements which are not zero-divisors. Moreover, we have constructed some new families of integrally indecomposable polytopes in \mb giving infinite families of absolutely irreducible multivariate polynomials over arbitrary fields.
Integral polytopes, integral indecomposability, multivariate polynomials, absolute irreducibility
"Integral polytopes and polynomial factorization,"
Turkish Journal of Mathematics: Vol. 37:
1, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss1/3