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 Rd, especially reptiles with holes. In particular, we construct, for each even integer n ≥ 4, an n-reptile in R2 with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of infinitely many components.

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