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    Protasov, Igor and Protasova, Ksenia 2014. Kaleidoscopical configurations. Journal of Mathematical Sciences, Vol. 200, Issue. 3, p. 352.

    Srivastava, S.M. and Thangadurai, R. 2005. On Steinhaus sets. Expositiones Mathematicae, Vol. 23, Issue. 2, p. 171.


Survey of the Steinhaus Tiling Problem

  • Steve Jackson (a1) and R. Daniel Mauldin (a1)
  • DOI:
  • Published online: 15 January 2014

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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