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.
Shuffle Theorems and Sandpiles
D'Adderio M.;Iraci A.;Vanden Wyngaerd A.
2025-01-01
Abstract
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.File in questo prodotto:
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