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Journal of the Ramanujan Mathematical Society

Volume 36, Issue 2, June 2021  pp. 123–127.

Combinatorial interpretations of q-series using n-color partitions

Authors:  M. Rana and N. Saikia
Author institution:School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, Punjab, India

Summary:  We give combinatorial interpretations of q-series G{1}(q) and G{2} (q) given by G{1} (q) := ∑ {{n=0}}{∞} {(-1;q) {n} (-1){n} q{{n(n+1)/2}}}/{(q;q){n} (-q;q){n}} and G{2}(q) := ∑ {{n=0}}{∞} {(-1){n} q{{n(n+1)/2}}}/{(q;q){n}} using n-color partitions and discuss their arithmetic properties.

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