Matrix theoretic interpretations of some basic series identities (Q2906712)

Using a partition theoretical construction of Agarwal and Andrews -- the so-called \((n+t)\)-color partitions -- the authors give new combinatorial proof of the \(q\)-identities NEWLINENEWLINE\[NEWLINE\begin{aligned}\sum_{n=0}^{\infty} \frac{q^{3n^2-2n}}{(q;q^2)_n(q^4;q^4)_n}&=\frac{(-q,-q^5,-q^9;q^{10})_{\infty}}{(q^2,q^8;q^{10})_{\infty}},\\ \sum_{n=0}^{\infty}\frac{q^{2n^2}}{(q;q^2)_n(q^4;q^4)_n} &=\frac{(-q^3,-q^7,-q^{11};q^{14})_{\infty}}{(q^2,q^6,q^8,q^{12};q^{14})_{\infty}},\\ \sum_{n=0}^{\infty}\frac{q^{2n(n+1)}}{(q;q^2)_n(q^4;q^4)_n} &=\frac{(-q^5,-q^7,-q^9;q^{14})_{\infty}}{(q^4,q^6,q^8,q^{10};q^{14})_{\infty}}\end{aligned}NEWLINE\]NEWLINE of Rogers, Selberg and Bailey.