Root Geometry of Polynomial Sequences I: Type (0, 1)
نویسندگان
چکیده
This paper is concerned with the distribution in the complex plane of the roots of a polynomial sequence {Wn(x)}n≥0 given by a recursion Wn(x) = aWn−1(x) + (bx + c)Wn−2(x), with W0(x) = 1 and W1(x) = t(x − r), where a > 0, b > 0, and c, t, r ∈ R. Our results include proof of the distinct-real-rootedness of every such polynomial Wn(x), derivation of the best bound for the zero-set {x | Wn(x) = 0 for some n ≥ 1}, and determination of three precise limit points of this zero-set. Also, we give several applications from combinatorics and topological graph theory.
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