Lee, Thomas2025-04-282025-04-282025-04-282025-04-25https://hdl.handle.net/10012/21660We formally extend the theory of polynomial capacity to power series and totally uni- modular matrices. Using these results, we prove the log-asymptotic correctness of bounds by Brändén, Leake, and Pak developed through the use of Lorentzian polynomials ([BLP23]) under certain conditions, and provide a counterexample where these bounds are not log- asymptotically correct, even when symmetry exists.enlattice pointscontingency tablespolynomial capacityenumerationasymptoticsgenerating functionsconvex optimizationMaster Thesis