“…Let us also mention that there are many related papers that study lower-dimensional subsets of the Euclidean space [1,6,33,36,38,31,32,59,37], subsets of the multidimensional integer lattice [49,5,46], or patterns with arithmetic structure [44,39,34,51,25,10,17,16,11,24,15]. We do not discuss these types of results here.…”