Abstract
This paper continues the study initiated by Alex Heinis of the set H of pairs (α,β) obtained as the lower and upper limit of the ratio of complexity and length for an infinite word. Heinis proved that this set contains no point under a certain curve. We extend this result by proving that there are only three points on this curve, namely (1,1), (3/2, 5/3) and (2,2), and moreover the point (3/2, 5/3) is an isolated point in the set H. For this, we use Rauzy graphs, generalizing techniques of Ali Aberkane.
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