递推关系式与二元欧拉多项式的乘积

付梅, 胡浩栋

数学学报 ›› 2021, Vol. 64 ›› Issue (6) : 1037-1042.

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数学学报 ›› 2021, Vol. 64 ›› Issue (6) : 1037-1042. DOI: 10.12386/A2021sxxb0086
论文

递推关系式与二元欧拉多项式的乘积

    付梅1, 胡浩栋2
作者信息 +

A Recurrence Relation and the Product of Two Bivariate Eulerian Polynomials

    Mei FU1, Hao Dong HU2
Author information +
文章历史 +

摘要

对满足某类递推关系式的数列,我们用完全齐次对称函数表示了它的生成函数,并结合该生成函数与上下文无关文法,给出了两重二元欧拉多项式乘积一个简洁的展开式.

Abstract

We translate a recurrence relation into a generating function and expand the product of two bivariate Eulerian polynomials in terms of the complete homogeneous symmetric functions.

关键词

递推关系式 / 完全齐次对称函数 / 上下文无关文法 / 欧拉多项式

Key words

recurrence / complete homogeneous symmetric function / context-free grammar / Eulerian polynomial

引用本文

导出引用
付梅, 胡浩栋. 递推关系式与二元欧拉多项式的乘积. 数学学报, 2021, 64(6): 1037-1042 https://doi.org/10.12386/A2021sxxb0086
Mei FU, Hao Dong HU. A Recurrence Relation and the Product of Two Bivariate Eulerian Polynomials. Acta Mathematica Sinica, Chinese Series, 2021, 64(6): 1037-1042 https://doi.org/10.12386/A2021sxxb0086

参考文献

[1] Carlitz L., Product of two Eulerian polynomials, Math. Mag., 1963, 36(1):37-41.
[2] Chen W. Y. C., Context-free grammars, differential operators and formal power series, Theoret. Comput. Sci., 1993, 117(1-2):113-129.
[3] Chen W. Y. C., Fu A. M., Context-free grammars for permutations and increasing trees, Adv. in Appl. Math., 2017, 82:8-82.
[4] Dumont D., William chen grammars and derivations in trees and arborescences, Sém. Lothar. Combin., 1996, 37:B37a, 21 pp.
[5] Kim D. S., Kim T., Lee S. H., et al., Some identities for the product of two bernoulli and euler polynomials, Adv. in Difference Equations, 2012, 2012:95 pp.
[6] Ma S. M., Ma J., Yeh Y. N., γ-positivity and partial γ-positivity of descent-type polynomials, J. Combinatorial Theory, Ser. A, 2019, 167:257-293.
[7] Pan H., Sun Z. W., New identities involving bernoulli and euler polynomials, J. Combinatorial Theory, Ser. A, 2006, 113:156-175.

基金

国家自然科学基金资助项目(11831002,71771141)

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