New Multiplier Sequences via Discriminant Amoebae

Details New Multiplier Sequences via Discriminant Amoebae New Multiplier Sequences via Discriminant Amoebae

2010-01-24

arxiv.org/abs/1001.4076v1

Mathematics

Algebraic Geometry

11 pages, 6 figures. Submitted for publication

Scientific paper

In their classic 1914 paper, Polya and Schur introduced and characterized two types of linear operators acting diagonally on the monomial basis of R[x], sending real-rooted polynomials (resp. polynomials with all nonzero roots of the same sign) to real-rooted polynomials. Motivated by fundamental properties of amoebae and discriminants discovered by Gelfand, Kapranov, and Zelevinsky, we introduce two new natural classes of polynomials and describe diagonal operators preserving these new classes. A pleasant circumstance in our description is that these classes have a simple explicit description, one of them coinciding with the class of log-concave sequences.

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