Shuffle Theorems and Sandpiles

We provide an explicit description of the recurrent configurations of the sandpile model on a family of graphs G^μ,ν, which we call clique-independent graphs, indexed by two compositions μ and ν. 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 ⟨∇en,eμhν⟩ in terms of these configurations.