Abstract
A weak square in a binary word is a pair of adjacent nonempty blocks of the same length, having the same number of Is. A weak circular square is a weak square which is possibly wrapped around the word: the tail protruding from the right end of the word reappears at the left end. Two weak circular squares are equivalent if they have the same length and contain the same number of ones. We prove that the longest word with only 2κ inequivalent weak circular squares contains 42κ + 2 bits and has the form (01)2κ+1 or its complement. Possible connections to tandem repeats in the human genome are pointed out.
Cite
CITATION STYLE
Fraenkel, A. S., Simpson, J., & Paterson, M. (1997). On weak circular squares in binary words. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1264, pp. 76–82). Springer Verlag. https://doi.org/10.1007/3-540-63220-4_51
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