This thesis concerns certain inequalities and asymptotic formulas in algebraic combinatorics. It consists of two separate parts. The first part studies inequalities concerning triangular-grid billiards and plabic graphs of Lam–Postnikov essential dimension 2. The material in this part is based on joint work with Colin Defant. The second part studies inequalities and asymptotic formulas concerning large-scale rook placements.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
