Polynomials with Real Zeros and Compatible Sequences
Keyword(s):
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.
1972 ◽
Vol 18
(2)
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pp. 129-136
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1992 ◽
pp. 113-120
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1998 ◽
Vol 45
(9)
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pp. 1010-1011
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2017 ◽
Vol E100.A
(12)
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pp. 2764-2775
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