On function compositions that are polynomials

2015/09/01 by Erhard Aichinger
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Algebraically closed field #Classical orthogonal polynomials #Composition (language) #Discrete orthogonal polynomials #Function (biology) #Orthogonal polynomials #Polynomial #math.AC #msc:12E05 #msc:13B25

paper · pdf · doi:10.1216/jca-2015-7-3-303

published as Journal of Commutative Algebra, Vol. 7, Number 3, pp. 303-315 (2015)

openalex publication_date 2015/09/01 · arxiv created 2016/01/08 · openalex created_date 2016/06/24 · arxiv updated 2019/09/04 · openalex updated_date 2026/08/05

Abstract

For a polynomial map \tupBoldf : kⁿ → k^m (k a field), we investigate those polynomials g ∈ k[t₁,…, t_n] that can be written as a composition g = h ∘ \tupBoldf, where h: k^m → k is an arbitrary function. In the case that k is algebraically closed of characteristic~0 and \tupBoldf is surjective, we will show that g = h ∘ \tupBoldf implies that h is a polynomial.

Citations

• Algebraic Geometry