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Characterization of two-distance sequences. (English) Zbl 0759.11005

If the reader has already heard at least one of the expressions: two- distance sequences, linear sequence, characteristic sequences, Beatty sequences, mechanical sequences, Fibonacci sequences, cutting sequences, Markoff spectrum, Sturmian trajectories, chain-codes, quasicrystals, species…or if he or she plays (two-dimensional) billiard, he will definitely enjoy the paper under review, where all these notions are described, studied and compared. The subject is very rich but the length of the paper is reasonable, and the reader will be delighted by this “promenade”.
The bibliography is wisely reduced to 22 titles [one of which, K. B. Stolarsky, Can. Math. Bull. 19, 473-482 (1976; Zbl 0359.10028), itself contains an impressive bibliography]. Finally the curious reader might try to follow the attempts of the authors towards a classification of \(f\)-distance sequences for \(f>2\).

MSC:

11B99 Sequences and sets
05B99 Designs and configurations
68R05 Combinatorics in computer science

Citations:

Zbl 0359.10028
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