Three overlapping squares: The general case characterized & applications

The “Three Squares Lemma” [9] famously explored the consequences of supposing that three squares occur at the same position in a string; essentially it showed that this phenomenon could not occur unless the longest of the three squares was at least the sum of the lengths of the other two. More recently, several papers [10,30,21,13] have greatly extended this result to a “New Periodicity Lemma” (NPL) by supposing that only two of the squares …