Year: 2020
Type: article
Abstract: We give a new and constructive proof of the existence of a large class of univariate polynomials whose graphs have preassigned shapes. By definition, all the critical points of a Morse polynomial function are real and simple and all its critical values are distinct. Thus to any Morse polynomial we can associate an alternating permutation called Arnold snake , given by the relative positions of its critical values. Our main result is an effective construction that can realise any separable alternating permutation as the Arnold snake of a Morse polynomial.
Source: Portugaliae Mathematica
DOI: 10.4171/pm/2050
Author: Miruna-Ştefana Sorea
Institution: Max Planck Institute for Mathematics in the Sciences
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2939019102