# 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

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