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Geometrical Bijections in Discrete Lattices
| Content Provider | Scilit |
|---|---|
| Author | Carstens, Hans-Georg Deuber, Walter A. Thumser, Wolfgang Koppenrade, Elke |
| Copyright Year | 1999 |
| Description | We define uniformly spread sets as point sets in d-dimensional Euclidean space that are wobbling equivalent to the standard lattice $ℤ^{d}$. A linear image $ϕ(ℤ^{d}$) of $ℤ^{d}$ is shown to be uniformly spread if and only if det(ϕ) = 1. Explicit geometrical and number-theoretical constructions are given. In 2-dimensional Euclidean space we obtain bounds for the wobbling distance for rotations, shearings and stretchings that are close to optimal. Our methods also allow us to analyse the discrepancy of certain billiards. Finally, we take a look at paradoxical situations and exhibit recursive point sets that are wobbling equivalent, but not recursively so. |
| Related Links | http://pdfs.semanticscholar.org/51fc/e06406f9ab40d55f073c0af2a135ac3264e8.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5E365978913D1A11AAFDA416D156ACD3/S0963548398003484a.pdf/div-class-title-geometrical-bijections-in-discrete-lattices-div.pdf |
| Ending Page | 129 |
| Page Count | 21 |
| Starting Page | 109 |
| ISSN | 09635483 |
| e-ISSN | 14692163 |
| DOI | 10.1017/s0963548398003484 |
| Journal | Combinatorics, Probability and Computing |
| Issue Number | 1-2 |
| Volume Number | 8 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1999-01-01 |
| Access Restriction | Open |
| Subject Keyword | Combinatorics, Probability and Computing Artificial Intelligence Point Sets |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics |
