#### Title

Reptiles with Holes

#### Document Type

Article

#### Publication Date

10-2005

#### Publication Title

Proceedings of the Edinburgh Mathematical Society

#### DOI

10.1017/S001309150400001X

#### ISSN

1464-3839

#### Abstract

Croft, Falconer and Guy asked: what is the smallest integer *n* such that an *n*-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in *R ^{d}*, especially reptiles with holes. In particular, we construct, for each even integer

*n*≥ 4, an

*n*-reptile in

*R*with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of inﬁnitely many components.

^{2}#### Recommended Citation

Jordan, Francis, Sze-Man Ngai.
2005.
"Reptiles with Holes."
*Proceedings of the Edinburgh Mathematical Society*, 48 (3): 651-671.
doi: 10.1017/S001309150400001X source: https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/reptiles-with-holes/7B77AE5C796E5FD04E67F2107967C9FD

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/598