Mathematics Colloquia and Seminars

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Chapoton triangles are polynomials in two variables defined by Coxeter-Catalan objects. These polynomials are related by some remarkable identities that only depend on the rank of the associated (finite) Coxeter system. The multidimensional Catalan numbers enumerate the number of standard Young tableaux of a rectangular shape. It also counts the number the vertices of a polytope known as the Grassmann associahedron. Using the structure of this polytope, I will give analogues of the Chapoton triangles and present a conjecture that they are related by the same identities as in the Coxeter setting. This is based on joint work with Alexander Garver.