Title: Steinhaus Sets and Jackson Sets
Authors: Su Gao, Arnold W. Miller, and William A. R. Weiss
Abstract: We prove that there does not exist a subset of the
plane S that meets every isometric copy of the vertices of the
unit square in exactly one point. We give a complete
characterization of all three point subsets F of the reals such
that there does not exists a set of reals S which meets every
isometric copy of F in exactly one point. A finite set X in the
plane is Jackson iff for every subset S of the plane there
exists an isometric copy Y of X such that Y does not meets S in
exactly one point. These results are related to the open
problem:
Q. (Steve Jackson) Is every finite set X in the plane of two or
more points Jackson?
Latex2e: 23 pages
Latest version at: www.math.wisc.edu/~miller