Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.4169/amer.math.monthly.118.08.743 | AMERICAN MATHEMATICAL MONTHLY |
Keywords | Field | DocType |
null | Picard–Lindelöf theorem,Combinatorics,Algebra,Brouwer fixed-point theorem,Bounded set,Mean value theorem,Mean value theorem (divided differences),Mathematics,Fixed-point theorem,Siegel's theorem on integral points,Lagrange's theorem (group theory) | Journal |
Volume | Issue | ISSN |
118 | 8 | 0002-9890 |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Penghao Cao | 1 | 0 | 0.34 |
| Liping Yuan | 2 | 21 | 5.07 |