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Overlap-freeness in infinite partial words

By et al. Vesa Havala


We prove that there exist infinitely many infinite overlap-free binary partial words. Moreover, we show that these words can contain only one hole and the hole must occur either in the first or in the second position. We define that a partial word is k-overlap-free if it does not contain a factor of the form xyxyx where the length of x is at least k. We prove that there exist infinitely many binary partial words with an infinite number of holes which are 2-overlap-free

Topics: 19
Year: 2008
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