On 3-way combinatorial identities

Proceedings of the Indian Academy of Sciences. Mathematical sciences

A K AGARWAL^1¹  MEGHA GOYAL^2² 

[1] Center for Advanced Study in Mathematics, Panjab University, Chandigarh 160 014, India^1;Department of Basic and Applied Sciences, University College of Engineering, Punjabi University, Patiala 147 002, India^2

关键词: Basic series;    $n$-color partitions;    lattice paths;    associated lattice paths;    combinatorial identities;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, we provide combinatorial meanings to two generalized basic series with the aid of associated lattice paths. These results produce two new classes of infinite 3-way combinatorial identities. Five particular cases are also discussed. These particular cases provide new combinatorial versions of Göllnitz–Gordon identities and Göllnitz identity. Seven $q$-identities of Slater and five $q$-identities of Rogers are further explored using the same combinatorial object. These results are an extension of the work of Goyal and Agarwal (Utilitas Math. 95 (2014) 141–148), Agarwal and Rana (Utilitas Math. 79 (2009) 145–155), and Agarwal (J. Number Theory 28 (1988) 299–305).

【 授权许可】

CC BY