A unified approach to polynomial sequences with only real zeros

被引：107

作者：

Liu, Lily L. ^{[1
]}

Wang, Yi ^{[1
]}

机构：

[1] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS | 2007年 / 38卷 / 04期

基金：

美国国家科学基金会;

关键词：

polynomials withonly real zeros; polynomial sequences; recurrence relations;

D O I：

10.1016/j.aam.2006.02.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：542 / 560

页数：19

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