Generalized -expansions, substitution tilings, and local finiteness

  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},
  • N. P. Frank, E. A. Robinson, Jr..
  • 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
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