Finite configurations in sparse sets

Vincent Chan, Izabella Laba, Malabika Pramanik

Let $E\subseteq R^n$ be a closed set of Hausdorff dimension $\alpha$. For $m\ge n$, let $\{B_1,\dots ,B_k\}$ be $n\times (m-n)$ matrices. We prove that if the system of matrices $B_…