Séminaire Lotharingien de Combinatoire, 91B.70 (2024), 12 pp.
Michele D'Adderio, Mark Dukes, Alessandro Iraci, Alexander Lazar, Yvan Le Borgne and Anna Vanden Wyngaerd
Shuffle Theorems and Sandpiles
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.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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