Quantitative bounds for product of simplices in subsets of the unit cube

Polona Durcik, Mario Stipčić

For each $1\le i\le n$, let $k_i\ge 1$ and let ${\Delta }_i$ be a set of vertices of a non-degenerate simplex of $k_i+1$ points in ${\mathbb{R}}^{k_i+1}$. If $A\subseteq [0,1]^{k_1+1}\tim…