On a generalized basic series and Rogers-Ramanujan type identities


  • P. Sonik IK Gujral Punjab Technical University
  • D. Ranganatha Central University of Karnataka
  • Megha Goyal IK Gujral Punjab Technical University


In this paper, we give the generalization of MacMahon's type combinatorial identities. A generalized $q$-series is interpreted as the generating function of two different combinatorial objects, viz., restricted $n$-color partitions and weighted lattice paths which give entirely new Rogers–Ramanujan–MacMahon type combinatorial identities. This result yields an infinite class of 2-way combinatorial identities which further extends the work of Agarwal and Goyal. We also discuss the bijective proof of the main result. Forbye, eight particular cases are also discussed which give a combinatorial interpretation of eight entirely new Rogers–Ramanujan type identities.

Author Biographies

P. Sonik, IK Gujral Punjab Technical University

Research Scholar, 

Department of Mathematical Sciences

D. Ranganatha, Central University of Karnataka

Assistant Professor

Department of Mathematics

Megha Goyal, IK Gujral Punjab Technical University

Assistant Professor,

Basic and Applied Sciences