Counting convex shapes
| dc.contributor.author | Wise, Elitza | |
| dc.date.accessioned | 2024-09-13T22:42:24Z | |
| dc.date.available | 2024-09-13T22:42:24Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | This research project aimed to examine C(n), the number of convex connected subsets of lattice containing n points. The primary objective was to derive and analyse an upper bound for C(n) to determine whether it grows sub-exponentially. This was done by programming a recursive code that took n as input and constructed every convex connected shape row-by-row. To ensure the results of C(n) were correct, the shapes were visually printed as output and further studied. This included focusing on pairs of adjacent C(n) and C(n+1) values, and confirming that the number of ways to add a point to the n-shapes was equal to the number of ways to take away a point from the (n+1)-shapes. Using a log-log regression transformation it was confirmed that C(n) is, in fact, sub-exponential. This plays a role in problems in statistical mechanics. | |
| dc.description.reviewstatus | Reviewed | |
| dc.description.scholarlevel | Undergraduate | |
| dc.description.sponsorship | Valerie Kuehne Undergraduate Research Awards (VKURA) | |
| dc.identifier.uri | https://hdl.handle.net/1828/20415 | |
| dc.language.iso | en | |
| dc.publisher | University of Victoria | |
| dc.subject | convexity | |
| dc.subject | enumeration | |
| dc.subject | asymptotics | |
| dc.subject | lattice | |
| dc.subject | recursion | |
| dc.subject | sub-exponential growth | |
| dc.title | Counting convex shapes | |
| dc.type | Poster |