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pro vyhledávání: '"CHEN Dandan"'
In 2007, Andrews and Paule introduced the family of functions $\Delta_k(n)$, which enumerate the number of broken $k$-diamond partitions for a fixed positive integer $k$. In 2013, Radu and Sellers completely characterized the parity of $\Delta_3(8n +
Externí odkaz:
http://arxiv.org/abs/2412.04998
Autor:
Chen, Dandan, Zou, Ziyin
Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding combinatorial pro
Externí odkaz:
http://arxiv.org/abs/2410.14126
In 2021, Andrews mentioned that George Beck introduced partition statistics $M_w(r,m,n)$, which denote the total number of ones in the partition of $n$ with crank congruent to $r$ modulo $m$. Recently, a number of congruences and identities involving
Externí odkaz:
http://arxiv.org/abs/2410.08450
Autor:
Chen, Dandan, Anderson, Carolyn
Categorical data are common in educational and social science research; however, methods for its analysis are generally not covered in introductory statistics courses. This chapter overviews fundamental concepts and methods in categorical data analys
Externí odkaz:
http://arxiv.org/abs/2409.02942
Autor:
Chen, Dandan, Liu, Zhiguo
In this paper, we establish a $q$-integral formula by using the orthogonality relation, and also provide a new proof of the $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials. A new $q$-beta integral with five parameters is
Externí odkaz:
http://arxiv.org/abs/2408.04444
Autor:
Chen, Dandan, Yin, Siyu
Publikováno v:
SIGMA 20 (2024), 103, 6 pages
We prove four new Rogers-Ramanujan-type identities for double series. They follow from the classical Rogers-Ramanujan identities using the constant term method and properties of Rogers-Szeg\H{o} polynomials.
Externí odkaz:
http://arxiv.org/abs/2408.00377
Autor:
Chen, Dandan, Yin, Siyu
In this paper we establish $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials, which was considered by Gasper. Additionally, we evaluate a new $q$-beta integral with several parameters.
Externí odkaz:
http://arxiv.org/abs/2407.17717
It is well known that Ramanujan conjectured congruences modulo powers of $5$, $7$ and and $11$ for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved congruences modulo pow
Externí odkaz:
http://arxiv.org/abs/2407.07107
Publikováno v:
International Journal of Qualitative Studies on Health & Well-Being. Dec2024, Vol. 19 Issue 1, p1-12. 12p.
Autor:
Hu, Haolong a, Zhou, Wei a, ⁎, Liu, Xiaoyang b, ⁎, Guo, Guanlin b, He, Yinhai b, Zhu, Leming c, Chen, Dandan a, Miao, Ruixue b
Publikováno v:
In Science of the Total Environment 10 January 2025 959