Self-affine tiles in ℝn

@article{Lagarias1996SelfaffineTI,
  title={Self-affine tiles in ℝn},
  author={J. Lagarias and Y. Wang},
  journal={Advances in Mathematics},
  year={1996},
  volume={121},
  pages={21-49}
}
  • J. Lagarias, Y. Wang
  • Published 1996
  • Mathematics
  • Advances in Mathematics
  • Abstract A self-affine tile in R n is a set T of positive measure with A ( T )=∪ d ∈ D ( T + d ), where A is an expanding n × n real matrix with |det( A )|= m an integer, and D ={ d ,  d 2 , ...,  d m }⊆ R n is a set of m digits. It is known that self-affine tiles always give tilings of R n by translation. This paper extends known characterizations of digit sets D yielding self-affine tiles. It proves several results about the structure of tilings of R n possible using such tiles, and gives… CONTINUE READING
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