Open Access
2010/2011 Full Dimensional Sets Without Given Patterns
Péter Maga
Real Anal. Exchange 36(1): 79-90 (2010/2011).


We construct a $d$ Hausdorff dimensional compact set in $\R^d$ that does not contain the vertices of any parallelogram. We also prove that for any given triangle ($3$ given points in the plane) there exists a compact set in $\R^2$ of Hausdorff dimension $2$ that does not contain any similar copy of the triangle. On the other hand, we show that the set of the $3$-point patterns of a $1$-dimensional compact set of $\R$ is dense.


Download Citation

Péter Maga. "Full Dimensional Sets Without Given Patterns." Real Anal. Exchange 36 (1) 79 - 90, 2010/2011.


Published: 2010/2011
First available in Project Euclid: 14 March 2011

zbMATH: 1246.28005
MathSciNet: MR3016405

Primary: 28A78

Keywords: avoiding patterns , Hausdorff dimension

Rights: Copyright © 2010 Michigan State University Press

Vol.36 • No. 1 • 2010/2011
Back to Top