科研之友
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摘要
Let H be the set of vertices of a tiling of the plane by regular hexagons of unit area. A point of H is called an H-point. Let [s] denote the greatest integer less than or equal to s, and let {s} = s - [s]. In this paper we prove a Blichfeldt-type theorem for H-points. It is shown that for any bounded set D subset of R(2) of area s, if 0 <= {s} < 1/3, then D can be translated so as to cover at least 2[s] + 1 H-points; if 1/3 <= {s} < 1, then by a translation D can be made to cover at least 2[s] + 2 H-points. Furthermore, we show that the results obtained are the best possible.
- 出版日期2011-10
- 单位河北师范大学
