  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.
