A note on the number of squares in a word

Authors:
Lucian Ilie
Affiliations:
Department of Computer Science, University of Western Ontario, London, Ontario, N6A 5B7, Canada
Venue:
Theoretical Computer Science
Year:
2007

Citing 5
Cited 15

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Abstract

Fraenkel and Simpson [A.S. Fraenkel, J. Simpson, How many squares can a string contain? J. Combin. Theory Ser. A 82 (1998) 112-120] proved that the number of squares in a word of length n is bounded by 2n. In this note we improve this bound to 2n-@Q(logn). Based on the numerical evidence, the conjectured bound is n.