A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On the number of frames in binary words
Tekijät: Harju T, Karki T
Kustantaja: ELSEVIER SCIENCE BV
Julkaisuvuosi: 2011
Journal: Theoretical Computer Science
Tietokannassa oleva lehden nimi: THEORETICAL COMPUTER SCIENCE
Lehden akronyymi: THEOR COMPUT SCI
Numero sarjassa: 39
Vuosikerta: 412
Numero: 39
Aloitussivu: 5276
Lopetussivu: 5284
Sivujen määrä: 9
ISSN: 0304-3975
DOI: https://doi.org/10.1016/j.tcs.2011.05.032
Tiivistelmä
A frame is a square uu, where u is an unbordered word. Let F(n) denote the maximum number of distinct frames in a binary word of length n. We count this number for small values of n and show that F(n) is at most left perpendicularn/2right perpendicular 8 for all n and greater than 7n/30 - epsilon for any positive epsilon and infinitely many n. We also show that Fibonacci words, which are known to contain plenty of distinct squares, have only a few frames. Moreover, by modifying the Thue-Morse word, we prove that the minimum number of occurrences of frames in a word of length n is inverted right perpendicularn/2inverted left perpendicular - 2. (C) 2011 Elsevier B.V. All rights reserved.
A frame is a square uu, where u is an unbordered word. Let F(n) denote the maximum number of distinct frames in a binary word of length n. We count this number for small values of n and show that F(n) is at most left perpendicularn/2right perpendicular 8 for all n and greater than 7n/30 - epsilon for any positive epsilon and infinitely many n. We also show that Fibonacci words, which are known to contain plenty of distinct squares, have only a few frames. Moreover, by modifying the Thue-Morse word, we prove that the minimum number of occurrences of frames in a word of length n is inverted right perpendicularn/2inverted left perpendicular - 2. (C) 2011 Elsevier B.V. All rights reserved.
Turun yliopiston Tutkimustietojärjestelmän portaali