Integral self-affine tiles in ℝn I. Standard and nonstandard digit sets

  title={Integral self-affine tiles in ℝn I. Standard and nonstandard digit sets},
  author={J. Lagarias and Y. Wang},
  journal={Journal of The London Mathematical Society-second Series},
  • J. Lagarias, Y. Wang
  • Published 1996
  • Mathematics
  • Journal of The London Mathematical Society-second Series
  • We investigate the measure and tiling properties of integral self-affine tiles, which are sets of positive Lebesgue measure of the form T(A,@) = { £ * x A~'d^: all d}€@}, where AeMn(Z) is an expanding matrix with |det (A)| = m, and Qs ^ 2" is a set of m integer vectors. The set Q> is called a digit set, and is called standard if it is a complete set of residues of Z"/A(Z") or arises from one by an integer affine transformation, and nonstandard otherwise. We prove that all sets T(A, Of) have… CONTINUE READING
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