Enumeration of Level-k Hypertriangulations

Author

Patrick J. Kaylor, The University of Texas Rio Grande Valley

Date of Award

8-1-2024

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Alexey Garber

Second Advisor

Luigi Ferraro

Third Advisor

Alexey Glazyrin

Abstract

Triangulations are a classical object in discrete and computational geometry that finds it uses in many other fields, including numerous applications. In this thesis we approach the question of enumerating all hypertriangulations of a point set, the family of tilings introduced by Olarte and Santos in 2022 as induced projections of hypersimplices. Unfortunately, the usual approach to enumeration of trinagulations using flips may not work for hypertriangulations as flip-connectivity is only conjectured for that family even in the two-dimensional case. As a result, we develop a DFS-based algorithm and present its Python implementation that enumerates all hypertriangulations of small point sets for all feasible levels k.

Comments

Copyright 2024 Patrick J. Kaylor. https://proquest.com/docview/3115400209

Recommended Citation

Kaylor, Patrick J., "Enumeration of Level-k Hypertriangulations" (2024). Theses and Dissertations. 1591.
https://scholarworks.utrgv.edu/etd/1591