Note on the monotonicity of coefficients for some \(q\)-series arising from Ramanujan's lost notebook
The author gives a partition-theoretic proof of the non-negativity of the coefficients in the power series expansion of \((q^p;q^p)_{\infty}/(q^r;q^p)_{\infty}(q^{p-r};q^p)_{\infty}\), \(1 \leq r < p\), and uses the crank of vector partitions to prove the almost-increasingness of the coefficients.
scientific article; zbMATH DE number 1406509