Rocky Mountain Journal of Mathematics

The real-rootedness of generalized Narayana polynomials related to the Boros-Moll polynomials

Herman Z.Q. Chen, Arthur L.B. Yang, and Philip B. Zhang

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Abstract

In this paper, we prove the real-rootedness of a family of generalized Narayana polynomials which arose in the study of the infinite log-concavity of the Boros-Moll polynomials. We establish certain recurrence relations for these Narayana polynomials, from which we derive the real-rootedness. In order to prove the real-rootedness, we use a sufficient condition due to Liu and Wang to determine whether two polynomials have interlaced zeros. The recurrence relations are verified with the help of the $Mathematica$ package $HolonomicFunctions$.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 1 (2018), 107-119.

Dates
First available in Project Euclid: 28 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1524880883

Digital Object Identifier
doi:10.1216/RMJ-2018-48-1-107

Mathematical Reviews number (MathSciNet)
MR3795735

Zentralblatt MATH identifier
1385.05014

Subjects
Primary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 26C10: Polynomials: location of zeros [See also 12D10, 30C15, 65H05]

Keywords
Generalized Narayana polynomials real zeros interlacing zeros

Citation

Chen, Herman Z.Q.; Yang, Arthur L.B.; Zhang, Philip B. The real-rootedness of generalized Narayana polynomials related to the Boros-Moll polynomials. Rocky Mountain J. Math. 48 (2018), no. 1, 107--119. doi:10.1216/RMJ-2018-48-1-107. https://projecteuclid.org/euclid.rmjm/1524880883


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