On 3-way combinatorial identities

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Abstract

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).

Keywords

Basic series n-color partitions lattice paths associated lattice paths combinatorial identities 

2010 Mathematics Subject Classification

05A15 05A17 11P81 

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Center for Advanced Study in MathematicsPanjab UniversityChandigarhIndia
  2. 2.Department of Basic and Applied SciencesUniversity College of Engineering, Punjabi UniversityPatialaIndia

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