A unified approach to polynomial sequences with only real zeros
A unified approach to polynomial sequences with only real zeros
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DOI：
10.1016/j.aam.2006.02.003
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发表时间：
2005-09
期刊：
影响因子：
--
通讯作者：
L. L. Liu-L.;Yi Wang
中科院分区：
文献类型：
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作者：
L. L. Liu-L.;Yi Wang
基于交错零点法，给出了多项式序列只有真实的零点的新的充分条件。作为应用，我们得到了几个著名的事实，包括现实的正交多项式，匹配多项式，纳拉亚纳多项式和欧拉多项式的零点。我们还解决了某些aptures的斯塔尔属多项式证明他们为某些类别的图，同时表明，他们是假的一般。
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.