Abstract
We present an approach to the problem of maximum number of distinct squares in a string which underlines the importance of considering as key variables both the length n and n − d where d is the size of the alphabet. We conjecture that a string of length n and containing d distinct symbols has no more than n − d distinct squares, show the critical role played by strings satisfying n = 2d, and present some properties satisfied by strings of length bounded by a constant times the size of the alphabet.
Supported in part by grants from the Natural Sciences and Engineering Research Council of Canada for the first 2 authors, and by the Canada Research Chair Programme and Mathematics of Information Technology and Complex Systems grants for the first author, and by Queen Elizabeth II Graduate Scholarship in Science and Technology for the third author.
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References
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Deza, A., Franek, F., Jiang, M. (2011). A d-Step Approach for Distinct Squares in Strings. In: Giancarlo, R., Manzini, G. (eds) Combinatorial Pattern Matching. CPM 2011. Lecture Notes in Computer Science, vol 6661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21458-5_9
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DOI: https://doi.org/10.1007/978-3-642-21458-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21457-8
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