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arXiv · 2307.03239

Hyperbolic polynomials and starved polytopes

Arne Lien
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Abstract

We study sets of univariate hyperbolic polynomials that share the same first few coefficients and show that they have a natural combinatorial description akin to that of polytopes. We define a stratification of such sets in terms of root arrangements of hyperbolic polynomials and show that any stratum is either empty, a point or of maximal dimension and in the latter case we characterise its relative interior. This is used to show that the poset of strata is a graded, atomic and coatomic lattice and to provide an algorithm for computing which root arrangements are realised in such sets of hyperbolic polynomials.

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Arne Lien. 2023-07-06. Hyperbolic polynomials and starved polytopes. https://arxiv.org/abs/2307.03239

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