2 citations · 2 across the 6 of their papers we have counts for
7 papers
Any-dimensional Positivstellensätze for symmetric functions
Sebastian Debus, Robin Schabert
Positivstellensätze provide certificates of positivity for polynomials. Extending these certificates to symmetric functions, uniformly across all dimensions, presents structural ch…
Deciding Connectivity in Symmetric Semi-Algebraic Sets
Cordian. Riener, Robin Schabert, Thi Xuan Vu
A semi-algebraic set is a subset of defined by a finite collection of polynomial equations and inequalities. In this paper, we investigate the problem of determining…
Constructively describing orbit spaces of finite groups by few inequalities
Philippe Moustrou, Cordian Riener, Robin Schabert
Let be a finite group acting linearly on . A celebrated Theorem of Procesi and Schwarz gives an explicit description of the orbit space as a…
Connectivity in Symmetric Semi-Algebraic Sets
Cordian Riener, Robin Schabert, Thi Xuan Vu
Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a…
Shellable slices of hyperbolic polynomials and the degree principle
Arne Lien, Robin Schabert
We study a natural stratification of certain affine slices of univariate hyperbolic polynomials. We look into which posets of strata can be realized and show that the dual of the p…
Slices of Stable Polynomials and Connections to the Grace-Walsh-Szegő theorem
Sebastian Debus, Cordian Riener, Robin Schabert
Univariate polynomials are called stable with respect to a domain if all of their roots lie in . We study linear slices of the space of stable univariate polynomials with re…
Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions
Cordian Riener, Robin Schabert
A real univariate polynomial of degree is called hyperbolic if all of its roots are on the real line. Such polynomials appear quite naturally in different applications, for…