In this paper, we introduce stable multivariate generalizations of Narayana polynomials of type A and type B. Our polynomials are multivariate generating polynomials over labeled plane trees and can be generated by a grammatical labeling based on a context-free grammar. Our proof of real stability uses a characterization of stable-preserving linear operators due to Borcea and Br\"and\'en.
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Yang et al. (2024) studied this question.
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