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This paper studies empty squares in arbitrary orientation among a set P of n points in the plane. We prove that the number of empty squares with four contact pairs is between Ω(n) and O(n²), and that these bounds are tight, provided P is in a certain general position. A contact pair of a square is a pair of a point p ∈ P and a side 𝓁 of the square with p ∈ 𝓁. The upper bound O(n²) also applies to the number of empty squares with four contact points, while we construct a point set among whichdoi:10.4230/lipics.socg.2020.13 dblp:conf/compgeom/BaeY20 fatcat:dqffcalnovbmfffwvif2kqkk7i