Abstract
What is the densest packing of points in an infinite strip of widthw, where any two of the points must be separated by distance at least I? This question was raised by Fejes-Tóth a number of years ago. The answer is trivial for\(w \leqslant \sqrt 3 /2\) and, surprisingly, it is not difficult to prove [M2] for\(w = n\sqrt 3 /2\), wheren is a positive integer, that the regular triangular lattice gives the optimal packing. Kertész [K] solved the case\(w< \sqrt 2 \). Here we fill the first gap, i.e., the maximal density is determined for\(\sqrt 3 /2< w \leqslant \sqrt 3 \).
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