Special Configurations in Anchored Rectangle Packings

2018/09/06 by Bian, Vincent
#05B40 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.01769

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.

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