Vol. 1, No. 1, 2008
Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 4, 805–1064
Issue 3, 549–803
Issue 2, 279–548
Issue 1, 1–278

Volume 17, 10 issues

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Construction of one-dimensional subsets of the reals not containing similar copies of given patterns

Tamás Keleti
Vol. 1 (2008), No. 1, 29–33
DOI: 10.2140/apde.2008.1.29
Abstract

For any countable collection of sets of three points we construct a compact subset of the real line with Hausdorff dimension 1 that contains no similar copy of any of the given triplets.

Keywords
Hausdorff dimension, avoiding patterns, Erdös similarity problem, similar copy, affine copy
Mathematical Subject Classification 2000
Primary: 28A78
Milestones
Received: 25 January 2008
Revised: 30 April 2008
Accepted: 30 May 2008
Published: 2 October 2008
Authors
Tamás Keleti
Department of Analysis
Eötvös Loránd University
Pázmány Péter sétány 1/C
H-1117 Budapest
Hungary
http://www.cs.elte.hu/analysis/keleti