Hyperbolic polynomials and starved polytopes

Author:

Arne Lien

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Combinatorics (math.CO), Representation Theory (math.RT)

journal:

date:

2023-07-05 16:00:00

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.

PDF: Hyperbolic polynomials and starved polytopes.pdf