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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