A note on the pyjama problem

Malikiosis, R.D. and Matolcsi, Máté and Ruzsa, Z. Imre (2013) A note on the pyjama problem. EUROPEAN JOURNAL OF COMBINATORICS, 34 (7). pp. 1071-1077. ISSN 0195-6698

Text A note on the pyjama problem.pdf Restricted to Repository staff only Download (396kB) | Request a copy

Abstract

This note concerns the so-called pyjama problem, whether it is possible to cover the plane by finitely many rotations of vertical strips of half-width ε. We first prove that there exist no periodic coverings for ε<13. Then we describe an explicit (non-periodic) construction for ε=1/3-1/48. Finally, we use a compactness argument combined with some ideas from additive combinatorics to show that finite coverings exist for all ε>1/5. The question whether ε can be arbitrarily small remains open. © 2013 Elsevier Ltd.

Actions (login required)

Edit Item