Algebraic and Enumerative Combinatorics Seminar | Jun Yan, Exact enumeration of lozenge tilings of a triangular region

Abstract: Tiling enumerations problems have fascinating connections with many other combinatorial problems involving perfect matchings, lattice paths, and determinants. In this talk, I will briefly survey some of the classical results and methods in this area. Then, I will present a new result enumerating lozenge tilings of a triangular region. Interestingly, the formula, reminiscent of the famous Kasteleyn formula counting domino tilings of the rectangle, contains roots of unity and does not obviously output an integer.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.