# Repetitions in Sturmian strings

Franěk, F., Karaman, A. and Smyth, W.F.
(2000)
*Repetitions in Sturmian strings.*
Theoretical Computer Science, 249
(2).
pp. 289-303.

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## Abstract

In this paper we apply a simple representation of Sturmian strings, which we call a “reduction sequence”, to three algorithms. The first algorithm accepts as input a given finite string x and determines in time whether or not x is Sturmian. The second algorithm is a modification of the first that, in the case that x is Sturmian, outputs a reduction sequence for a superstring u of x that is a prefix of an infinite Sturmian string. The third algorithm uses the reduction sequence of u to compute all the repetitions in u in time , thus extending a recent result for Fibonacci strings. The third algorithm is also based on a characterization of the repetitions in a Sturmian string that describes them compactly in terms of “runs”. Finally, for every integer r⩾4, we show how to construct an infinite Sturmian string that contains maximal repetitions of exponents 2,3,…,r−1, but none of exponent r.

Publication Type: | Journal Article |
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Publisher: | Elsevier BV |

Copyright: | © 2000 Elsevier Science B.V. |

URI: | http://researchrepository.murdoch.edu.au/id/eprint/27544 |

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