Spherical Recurrence and locally isometric embeddings of trees into positive density subsets of ${\mathbb{Z}}^d$

Kamil Bulinski

Magyar has shown that if $B\subset {\mathbb{Z}}^d$ has positive upper density $(d\ge 5)$, then the set of squared distances $\{\Vert b_1-b_2{\Vert }^2:b_1,b_2\in B\}$…