Abstract:Fraenkel and Simpson showed that the number of distinct squares in a word of
length n is bounded from above by 2n, since at most two distinct squares have
their rightmost, or last, occurrence begin at each position. Improvements by
Ilie to $2n-\Theta(\log n)$ and by Deza et al. to 11n/6 rely on the study of
combinatorics of FS-double-squares, when the maximum number of two last
occurrences of squares begin. In this paper, we first study how to maximize
runs of FS-double-squares in the prefix of a word. We show… Show more
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