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Title: A note on the pyjama problem
Authors: Malikiosis, R.D.
Matolcsi, M.
Ruzsa, I.Z.
Keywords: DRNTU::Science::Physics
Issue Date: 2013
Source: Malikiosis, R., Matolcsi, M., & Ruzsa, I. (2013). A note on the pyjama problem. European journal of combinatorics, 34(7), 1071-1077.
Series/Report no.: European journal of combinatorics
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<1/3. 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.
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.03.001
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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