# The Real-rootedness of Generalized Narayana Polynomials

@article{Chen2016TheRO, title={The Real-rootedness of Generalized Narayana Polynomials}, author={Herman Z. Q. Chen and Arthur L. B. Yang and Philip B. Zhang}, journal={arXiv: Combinatorics}, year={2016} }

In this paper, we prove the real-rootedness of two classes of generalized Narayana polynomials: one arising as the $h$-polynomials of the generalized associahedron associated to the finite Weyl groups, the other arising in the study of the infinite log-concavity of the Boros-Moll polynomials. For the former, Br\"{a}nd\'{e}n has already proved that these $h$-polynomials have only real zeros. We establish certain recurrence relations for the two classes of Narayana polynomials, from which we…

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