  We provide an explicit description of the recurrent configurations of the
sandpile model on a family of graphs $\widehat{G}_{\mu,\nu}$, which we call
clique-independent graphs, indexed by two compositions $\mu$ and $\nu$.
Moreover, we define a delay statistic on these configurations, and we show
that, together with the usual level statistic, it can be used to provide a new
combinatorial interpretation of the celebrated shuffle theorem of Carlsson and
Mellit. More precisely, we will see how to interpret the polynomials $\langle
\nabla e_n, e_{\mu}h_{\nu}\rangle$ in terms of these configurations.
