Geodesic
Polynomials with real zeros and compatible sequences
Li Liu1
1School of Mathematical Sciences Qufu Normal University
The electronic journal of combinatorics, Tome 19 (2012) no. 3

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Zbl
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.
DOI : 10.37236/2674
Classification : 26C10
Mots-clés : polynomials with only real zeros, compatible sequences, common interleaver

Li Liu  1

1 School of Mathematical Sciences Qufu Normal University 
Li Liu. Polynomials with real zeros and compatible sequences. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2674
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     author = {Li Liu},
     title = {Polynomials with real zeros and compatible sequences},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {3},
     doi = {10.37236/2674},
     zbl = {1253.26026},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2674/}
}
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