Note on powers in three interval exchange transformations

Details Note on powers in three interval exchange transformations Note on powers in three interval exchange transformations

2009-09-06

arxiv.org/abs/0909.1109v1

Mathematics

Combinatorics

7 pages

Scientific paper

We study repetitions in infinite words coding exchange of three intervals with permutation (3,2,1), called 3iet words. The language of such words is determined by two parameters $\varepsilon,\ell$. We show that finiteness of the index of 3iet words is equivalent to boundedness of the coefficients of the continued fraction of $\varepsilon$. In this case we also give an upper and lower estimate on the index of the corresponding 3iet word.

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