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1 results

  • Characterization of two-distance sequences

  • Part of
  • W. F. Lunnon, P. A. B. Pleasants
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 53 / Issue 2 / October 1992
    Published online by Cambridge University Press:
    09 April 2009, pp. 198-218
    Print publication:
    October 1992
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  • Three differently defined classes of two-symbol sequences, which we call the two-distance sequences, the linear sequences and the characteristic sequences, have been discussed by a number of authors and some equivalences between them are known. We present a self-contained proof that the three classes are the same (when ambiguous cases of linear sequences are suitably in terpreted). Associated with each sequence is a real invariant (having a different appropriate definition for each of the three classes). We give results on the relation between sequences with the same invariant and on the symmetry of the sequences. The sequences are closely related to Beatty sequences and occur as digitized straight lines and quasicrystals. They also provide examples of minimal word proliferation in formal languages.