# Generalized -expansions, substitution tilings, and local finiteness

```@article{Frank2008GeneralizedS,
title={Generalized -expansions, substitution tilings, and local finiteness},
author={N. P. Frank and E. A. Robinson and Jr..},
journal={Transactions of the American Mathematical Society},
year={2008},
volume={360},
pages={1163-1177}
}```
• Published 2008
• Mathematics, Physics
• Transactions of the American Mathematical Society
• For a fairly general class of two-dimensional tiling substitutions, we prove that if the length expansion β a Pisot number, then the tilings defined by the substitution must be locally finite. We also give a simple example of a two-dimensional substitution on rectangular tiles, with a non-Pisot length expansion β, such that no tiling admitted by the substitution is locally finite. The proofs of both results are effectively one-dimensional and involve the idea of a certain type of generalized… CONTINUE READING
35 Citations

#### References

SHOWING 1-10 OF 16 REFERENCES
Some Generalizations of the Pinwheel Tiling
• L. Sadun
• Mathematics, Computer Science
• Discret. Comput. Geom.
• 1998
• 34
• PDF
Dynamics of self-similar tilings
• 297
• Highly Influential
• PDF
Dynamics of Self-Similar Tilings, Ergodic Theory Dynamical Systems
• Errata, Ergodic Theory Dynamical Systems
• 1997
E-mail address: nafrank@vassar.edu Department of Mathematics
• E-mail address: nafrank@vassar.edu Department of Mathematics
• 2005
E-mail address: robinson@gwu
• E-mail address: robinson@gwu
Groups, Tilings, and Finite State Automata
• AMS Colloquium Lecture Notes
• 1989