Lower unitriangular totally nonnegative matrices generate real-rooted polynomials, enabling a general theory of chain enumeration in posets and a convex-hull characterization for hyperplane arrangement characteristic polynomials.
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Totally nonnegative matrices, chain enumeration and zeros of polynomials
Lower unitriangular totally nonnegative matrices generate real-rooted polynomials, enabling a general theory of chain enumeration in posets and a convex-hull characterization for hyperplane arrangement characteristic polynomials.