Shuffle Theorems, Sandpiles, and Lattice Paths

The shuffle theorem of Carlsson and Mellit proved a long-conejctured combinatorial formula for the coefficients of the symmetric function \nabla e_n in terms of statistics of lattice paths. In this talk I will discuss recent joint work with Michele D’Adderio (Università di Pisa), Mark Dukes (University College Dublin), Alessandro Iraci (Università Telematica Pigaso), Yvan Le Borgne (LaBRI Bordeaux), and Anna Vanden Wyngaerd (Université Libre de Bruxelles) in which we give a new interpretation of this symmetric function in terms of the combinatorial dynamics of the abelian sandpile model. Additionally, I will discuss possible connections to other lattice path models related to symmetric functions.

For information about the Richard P. Stanley Seminar in Combinatorics, visit… https://math.mit.edu/combin/