JeckLim

We show that if $L_1$ and $L_2$ are linear transformations from ${\mathbb{Z}}^d$ to ${\mathbb{Z}}^d$ satisfying certain mild conditions, then, for any finite subset $A$ of ${\mathbb{Z}}^d$, \ This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for many choices of $L_1$ and …