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ON THE NUMBER OF SQUARES IN PARTIAL WORDS




TekijätHarju Tero, Halava Vesa, Kärki Tomi

KustantajaEDP SCIENCES S A

Julkaisuvuosi2010

JournalRAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications

Tietokannassa oleva lehden nimiRAIRO-THEORETICAL INFORMATICS AND APPLICATIONS

Lehden akronyymiRAIRO-THEOR INF APPL

Numero sarjassa1

Vuosikerta44

Numero1

Aloitussivu125

Lopetussivu138

Sivujen määrä14

ISSN0988-3754

DOIhttps://doi.org/10.1051/ita/2010008


Tiivistelmä
The theorem of Fraenkel and Simpson states that the maximum number of distinct squares that a word w of length n can contain is less than 2n. 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 2k, where k is the size of the alphabet. Moreover, we prove that the number of distinct squares in a partial word with one hole and of length n is less than 4n, regardless of the size of the alphabet. For binary partial words, this upper bound can be reduced to 3n.


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