Wise, Elitza2024-09-132024-09-132024https://hdl.handle.net/1828/20415This 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.enconvexityenumerationasymptoticslatticerecursionsub-exponential growthPoster