On a generalized basic series and Rogers-Ramanujan type identities Article Swipe

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Pooja Sonik , D. Ranganatha , Megha Goyal ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.55016/ojs/cdm.v18i1.73025 · OA: W4390712995

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.

On a generalized basic series and Rogers-Ramanujan type identities Article Swipe

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