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Universal tilings of the plane by 0–1-matrices

✍ Scribed by Knut Dehnhardt; Heiko Harborth

Publisher: Elsevier Science
Year: 1988
Tongue: English
Weight: 673 KB
Volume: 73
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90133-1

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✦ Synopsis

A tiling of the plane by black and white unit squares of the square lattice is called (a, b)-universal if the tiling is built up by horizontal and vertical translations of a fundamental (m, n)-rectangle, and if every one of the possible 2ub different (a, b)-rectangles of black and white unit squares occurs somewhere in the tiling. If the fundamental (m, n)-rectangle is as small as possible (that is, with mn = 2"') then the tiling is called optimal (a, b)-universal. It is the purpose of this paper to prove the existence of optimal (a, b)-universal tilings for all a, b 5 2.

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