On the Number of Real Types of Univariate Polynomials
Symbolic Computation
2025-02-10 v1
Abstract
The real type of a finite family of univariate polynomials characterizes the combined sign behavior of the polynomials over the real line. We derive an explicit formula for the number of real types subject to given degree bounds. For the special case of a single polynomial we present a closed-form expression involving Fibonacci numbers. This allows us to precisely describe the asymptotic growth of the number of real types as the degree increases, in terms of the golden ratio.
Keywords
Cite
@article{arxiv.2502.04914,
title = {On the Number of Real Types of Univariate Polynomials},
author = {Nicolas Faroß and Thomas Sturm},
journal= {arXiv preprint arXiv:2502.04914},
year = {2025}
}