A unified approach to polynomial sequences with only real zeros
نویسندگان
چکیده
We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for certain classes of graphs, while showing that they are false in general. © 2006 Elsevier Inc. All rights reserved.
منابع مشابه
Ju l 2 00 6 A unified approach to polynomial sequences with only real zeros ∗
We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for cer...
متن کامل2 7 N ov 2 00 6 A unified approach to polynomial sequences with only real zeros ∗
We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for cer...
متن کاملPolynomial Sequences with Only Real Zeros
In this paper we develop methods to provide unified approaches to the reality of zeros of polynomial sequences satisfying certain recurrence relations and then apply them to derive some known results and solve certain open problems and conjectures.
متن کاملA Unified Approach for Design of Lp Polynomial Algorithms
By summarizing Khachiyan's algorithm and Karmarkar's algorithm forlinear program (LP) a unified methodology for the design of polynomial-time algorithms for LP is presented in this paper. A key concept is the so-called extended binary search (EBS) algorithm introduced by the author. It is used as a unified model to analyze the complexities of the existing modem LP algorithms and possibly, help ...
متن کاملPolynomials with only real zeros 1
Conditions which ensure that a combination of real polynomials, which have real interlacing zeros, continues to have only real zeros are derived. This gives a generalization of a result of Haglund and is proved using a unified method of Liu-Wang-Yeh.
متن کامل