A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
ON THE NUMBER OF SQUARES IN PARTIAL WORDS
Tekijät: Harju Tero, Halava Vesa, Kärki Tomi
Kustantaja: EDP SCIENCES S A
Julkaisuvuosi: 2010
Journal: RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications
Tietokannassa oleva lehden nimi: RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS
Lehden akronyymi: RAIRO-THEOR INF APPL
Numero sarjassa: 1
Vuosikerta: 44
Numero: 1
Aloitussivu: 125
Lopetussivu: 138
Sivujen määrä: 14
ISSN: 0988-3754
DOI: https://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.
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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