Special Configurations in Anchored Rectangle Packings

Abstract

Given a finite set S in [0, 1] 2 including the origin, an anchored rectangle packing is a set of non-overlapping rectangles in the unit square where each rectangle has a point of S as its left-bottom corner and contains no point of S in its interior. Allen Freedman conjectured in the 1960's one can always find an anchored rectangle packing with total area at least 1/2. We verify the conjecture for point configurations whose relative positions belong to certain classes of permutations.