Department of Mathematics Calendar
Thomas McConville, University of North Carolina at Greensboro, Chapoton triangles from multidimensional Catalan objects
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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. In this talk I will introduce some other combinatorial objects counted by these numbers. I will also 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.