Abstract
By using Chen, Hou and Mu’s extended Zeilberger algorithm, the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials. Based on these recurrence relations, the authors further prove the real-rootedness and asymptotic normality of Callan’s Narayana polynomials.
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Acknowledgements
We are grateful to the anonymous referees for their helpful comments and suggestions. We also would like to thank Qing-Hu Hou for his valuable comments, especially for showing us the extended Zeilberger algorithm is applicable in finding recurrence relations for certain combinatorial sequences.
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CHEN was supported by the National Natural Science Foundation of China under Grant No. 11601062. YANG was supported in part by the Fundamental Research Funds for the Central Universities and the National Natural Science Foundation of China under Grant Nos. 11522110 and 11971249, respectively. ZHAO was partially supported by the National Natural Science Foundation of China under Grant Nos. 11771330 and 11971203.
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Chen, X., Yang, A.L.B. & Zhao, J.J.Y. Recurrences for Callan’s Generalization of Narayana Polynomials. J Syst Sci Complex 35, 1573–1585 (2022). https://doi.org/10.1007/s11424-021-0216-z
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DOI: https://doi.org/10.1007/s11424-021-0216-z