The interlacing properties of generalized Narayana polynomials
Abstract
In this paper, we obtain two new interlacing properties on the zeros of a type of generalized Narayana polynomials arising in the study of the infinite log-concavity of the Boros$-$Moll polynomials. Our tools include a criterion established by Liu and Wang and two new recurrence relations for these Narayana polynomials. The new recurrences are verified with the help of ${\tt Maple}$ package ${\tt APCI}$ given by Hou.
Our results also imply the real-rootedness of these Narayana polynomials.
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Copyright (c) 2024 James Jing Yu Zhao
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