Displaying similar documents to “Infinite words containing squares at every position”

On the number of squares in partial words

Vesa Halava, Tero Harju, Tomi Kärki (2010)

RAIRO - Theoretical Informatics and Applications

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The theorem of Fraenkel and Simpson states that the maximum number of distinct squares that a word  of length  can contain is less than . This is based on the fact that no more than two squares can have their last occurrences starting at the same position. In this paper we show that the maximum number of the last occurrences of squares per position in a partial word containing one hole is , where is the size of the alphabet. Moreover, we prove that the number of distinct squares in...

Squares and overlaps in the Thue-Morse sequence and some variants

Shandy Brown, Narad Rampersad, Jeffrey Shallit, Troy Vasiga (2006)

RAIRO - Theoretical Informatics and Applications

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We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are -regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of ) contains an overlap.