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Survey of the Steinhaus Tiling Problem

  • Steve Jackson (a1) and R. Daniel Mauldin (a1)
Abstract
Abstract

We survey some results and problems arising from a classic problem of Steinhaus: Is there a subset S of ℝ2 such that each isometric copy of ℤ2 (the lattice points in the plane) meets S in exactly one point.

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[2] M. Ciucu , A remark on sets having the Steinhaus property, Combinatorica, vol. 16 (1996), pp. 321324.

[3] H. T. Croft , Three lattice point problems of Steinhaus, The Quarterly Journal of Mathematics. Oxford, vol. 33 (1982), pp. 7183.

[4] H. T. Croft , K. J. Falconer , and R. K. Guy , Unsolved problems in geometry, Springer-Verlag, New York, 1991.

[10] C. G. Gibson and P. E. Newstead , On the geometry of the planar 4-bar mechanism, Acta Applicandae Mathematicae, vol. 7 (1986), pp. 113135.

[13] S. Jackson and R. D. Mauldin , On a lattice problem of H. Steinhaus, Journal of the American Mathematical Society, vol. 15 (2002), pp. 817856.

[14] S. Jackson and R. D. Mauldin , Sets meeting isometric copies of a lattice in exactly one point, Proceedings of the National Academy of Sciences of the United States of America, vol. 99 (2002), pp. 1588315887.

[21] P. Komjáth , A lattice point problem of Steinhaus, The Quarterly Journal of Mathematics. Oxford, vol. 43 (1992), pp. 235241.

[22] R. D. Mauldin , On sets which meet each line in exactly two points, The Bulletin of the London Mathematical Society, vol. 30 (1998), pp. 397403.

[23] R. D. Mauldin and A. Q. Yingst , Comments on the Steinhaus tiling problem, Proceedings of the American Mathematical Society, vol. 131 (2003), pp. 20712079.

[24] Saharon Shelah , Can you take Solovay's inaccessible away?, Israel Journal of Mathematics, vol. 48 (1984), pp. 147.

[26] Robert M. Solovay , A model of set theory in which every set of reals is Lebesgue measurable, Annals of Mathematics, (1970), pp. 156.

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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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