Thesis (Ph. D.)--University of Rochester. Department of Mathematics, 2020.
We prove that fractal sets of high enough dimension contain a lot of configurations: If the Hausdorff dimension of a compact subset X of R^d, d≥2 is at least d d-1/k for some natural number k≥d+1 then [equation would not render] where H denotes the Hausdorff measure and X^k/E(d) the orbit space under the diagonal Euclidean action.
