Bad Pairs of Polynomial Zeros
Commun. Korean Math. Soc. 2000 Vol. 15, No. 4, 697-706
Seon-Hong Kim
Seoul National University
Abstract : If an arithmetic progression $F$ of length $2n$ and the number $k$ with $2k \leq n$ are given, can we find two monic polynomials with the same degrees whose set of all zeros form $F$ such that both the number of bad pairs and the number of nonreal zeros are $2k$? We will consider the case that both the number of bad pairs and the number of nonreal zeros are two. Moreover, we will see the fundamental relation between the number of bad pairs and the number of nonreal zeros, and we will show that the polynomial in $x$ where the coefficient of $x^k$ is the number of sequences having $2k$ bad pairs has all zeros real and negative.
Keywords : bad pairs, good pairs, zeros, polynomials
MSC numbers : Primary 30C15; Secondary 11B25
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd