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Restricted Steinhaus sets in the plane

Volume 238 / 2017

Devon Henkis, Steve Jackson, Jeff Lobe Fundamenta Mathematicae 238 (2017), 153-166 MSC: Primary 03E05; Secondary 05B99. DOI: 10.4064/fm260-7-2016 Published online: 23 March 2017

Abstract

For each prime $p$ we show the existence of a partial Steinhaus set in the plane for the prime $p$ which can be obtained from the points $\{ ({i/p}, {j/p}) : 0 \leq i,j \lt p\}$ by translating by integer amounts only in the horizontal direction. We raise several questions concerning these sets.

Authors

  • Devon HenkisDepartment of Mathematics
    University of North Texas
    Denton, TX 76203, U.S.A.
    e-mail
  • Steve JacksonDepartment of Mathematics
    University of North Texas
    Denton, TX 76203, U.S.A.
    e-mail
  • Jeff LobeDepartment of Mathematics
    University of North Texas
    Denton, TX 76203, U.S.A.
    e-mail

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