Restricted Steinhaus sets in the plane
Volume 238 / 2017
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.
