Packing polyominoes clumsily
| Autor: | Maria Axenovich, Torsten Ueckerdt, Stefan Walzer |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Mathematics::Combinatorics Control and Optimization Polyomino Plane (geometry) Computer Science Applications Condensed Matter::Soft Condensed Matter Set (abstract data type) Combinatorics Computational Mathematics Packing problems Computational Theory and Mathematics Aperiodic graph Circle packing Tetrahedron packing Maximal set Geometry and Topology Mathematics |
| Zdroj: | Computational Geometry. 47:52-60 |
| ISSN: | 0925-7721 |
| DOI: | 10.1016/j.comgeo.2013.08.011 |
| Popis: | For a set D of polyominoes, a packing of the plane with D is a maximal set of copies of polyominoes from D that are not overlapping. A packing with smallest density is called a clumsy packing. We give an example of a set D such that any clumsy packing is aperiodic. In addition, we compute the smallest possible density of a clumsy packing when D consists of a single polyomino of a given size and show that one can always construct a periodic packing arbitrarily close in density to the clumsy packing. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect