Polynomials with Real Zeros and Compatible Sequences
Polynomials with Real Zeros and Compatible Sequences
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DOI：
10.37236/2674
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发表时间：
2012-09
期刊：
影响因子：
--
通讯作者：
L. L. Liu-L.
中科院分区：
文献类型：
--
作者：
L. L. Liu-L.
本文基于相容零的方法，研究了只有实零的多项式。得到了两个前导系数符号相反的多项式相容的一个充分必要条件。作为应用，我们部分地回答了M. Chudnovsky和P. Seymour在最近的出版物[M。张志强，无爪图的独立多项式的根的研究。Ser的理论。[j].生物工程学报，2007,35(5):357—357。建立了两个多项式的交叠性质与相容性质之间的联系，并对一些已知的结果作了简单的证明。
In this paper, we study polynomials with only real zeros based on the method of compatible zeros. We obtain a necessary and sufficient condition for the compatible property of two polynomials whose leading coefficients have opposite sign. As applications, we partially answer a question proposed by M. Chudnovsky and P. Seymour in the recent publication [M. Chudnovsky, P. Seymour, The roots of the independence polynomial of a clawfree graph, J. Combin. Theory Ser. B 97 (2007) 350--357]. We also establish the connection between the interlacing property and the compatible property of two polynomials and give a simple proof of some known results.