The Real-rootedness of Generalized Narayana Polynomials

Autor:	Chen, Herman Z. Q., Yang, Arthur L. B., Zhang, Philip B.
Rok vydání:	2016
Předmět:	Mathematics - Combinatorics 05A15 26C10
Druh dokumentu:	Working Paper
Popis:	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 derive the real-rootedness. 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 \textit{HolonomicFunctions}. Comment: 14 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1602.00521 Zobrazit plný text záznamu View this record from Arxiv