J Austral Math Soc Ser A 53 pp198--218, 1992.

Characterization of Two-Distance Sequences

W. F. Lunnon and P. A. B. Pleasants

(Received 22 December 1989; revised 5 August 1991)

Abstract

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 interpreted). 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.

1991 AMS Subject Classification: 11B99, 05B99, 68R05, 68U05

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Authors

W. F. Lunnon: Department of Computer Science, St. Patrick's College, Maynooth, County Kildare, Eire.
P. A. B. Pleasants: School of Mathematics, Physics, Computing and Electronics, MacQuarie University, NSW 2109, Australia.

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Last Modified: Mon Feb 3 9:46:12 2003