Asymptotics of the number of lattice points in the transportation polytope via optimization on Lorentzian polynomials.
| dc.contributor.author | Lee, Thomas | |
| dc.date.accessioned | 2025-04-28T19:05:05Z | |
| dc.date.available | 2025-04-28T19:05:05Z | |
| dc.date.issued | 2025-04-28 | |
| dc.date.submitted | 2025-04-25 | |
| dc.description.abstract | We 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. | |
| dc.identifier.uri | https://hdl.handle.net/10012/21660 | |
| dc.language.iso | en | |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | lattice points | |
| dc.subject | contingency tables | |
| dc.subject | polynomial capacity | |
| dc.subject | enumeration | |
| dc.subject | asymptotics | |
| dc.subject | generating functions | |
| dc.subject | convex optimization | |
| dc.title | Asymptotics of the number of lattice points in the transportation polytope via optimization on Lorentzian polynomials. | |
| dc.type | Master Thesis | |
| uws-etd.degree | Master of Mathematics | |
| uws-etd.degree.department | Combinatorics and Optimization | |
| uws-etd.degree.discipline | Combinatorics and Optimization | |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | |
| uws.contributor.advisor | Leake, Jonathan | |
| uws.contributor.affiliation1 | Faculty of Mathematics | |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |