Steinhaus Sets and Jackson Sets

Su Gao; Arnold W. Miller; William A. R. Weiss

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arXiv · math/0603235

Steinhaus Sets and Jackson Sets

Su Gao·Arnold W. Miller·William A. R. Weiss

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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?

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BibTeX RIS

Su Gao, Arnold W. Miller, William A. R. Weiss. 2006-03-09. Steinhaus Sets and Jackson Sets. https://arxiv.org/abs/math/0603235

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