Name
Abstract | ||
|---|---|---|
A d-fold uniform covering of Rn by elementary shapes is a level d multiple tiling of Rn. The set of level values for which a prototile (a model shape) admits a multiple tiling is called the level semigroup of the prototile. In this paper we discuss the existence of prototiles with nontrivial level semigroups: for instance, does there exist a prototile admitting both tilings of levels 2 and 3, yet not admitting any tilings of level 1? The answer is yes--in fact, we show that for any a, b ∈ N there is a prototile whose level semigroup is exactly the set of nonnegative integer linear combinations of a and b. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1016/j.jcta.2003.12.005 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
d-fold uniform,level value,tiling,nontrivial level semigroups,nonnegative integer linear combination,multiple tiling,level semigroup,elementary shape,semigroup,model shape | Integer,Discrete mathematics,Linear combination,Combinatorics,Substitution tiling,Prototile,Semigroup,Mathematics | Journal |
Volume | Issue | ISSN |
106 | 1 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
2 | 0.62 | 1 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| John P. Steinberger | 1 | 329 | 18.30 |