Recurrences for Callan's Generalization of Narayana Polynomials

CHEN Xi, YANG Arthur Li Bo, ZHAO James Jing Yu

系统科学与复杂性(英文) ›› 2022, Vol. 35 ›› Issue (4) : 1573-1585.

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系统科学与复杂性(英文) ›› 2022, Vol. 35 ›› Issue (4) : 1573-1585. DOI: 10.1007/s11424-021-0216-z

Recurrences for Callan's Generalization of Narayana Polynomials

    CHEN Xi1, YANG Arthur Li Bo2, ZHAO James Jing Yu3
作者信息 +

Recurrences for Callan's Generalization of Narayana Polynomials

    CHEN Xi1, YANG Arthur Li Bo2, ZHAO James Jing Yu3
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文章历史 +

摘要

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.

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.

关键词

Asymptotic normality / Callan's Narayana polynomials / central limit theorem / local limit theorem / real zeros

Key words

Asymptotic normality / Callan's Narayana polynomials / central limit theorem / local limit theorem / real zeros

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CHEN Xi , YANG Arthur Li Bo , ZHAO James Jing Yu. Recurrences for Callan's Generalization of Narayana Polynomials. 系统科学与复杂性(英文), 2022, 35(4): 1573-1585 https://doi.org/10.1007/s11424-021-0216-z
CHEN Xi , YANG Arthur Li Bo , ZHAO James Jing Yu. Recurrences for Callan's Generalization of Narayana Polynomials. Journal of Systems Science and Complexity, 2022, 35(4): 1573-1585 https://doi.org/10.1007/s11424-021-0216-z

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基金

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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