A1 Refereed original research article in a scientific journal
On the number of frames in binary words
Authors: Harju T, Karki T
Publisher: ELSEVIER SCIENCE BV
Publication year: 2011
Journal: Theoretical Computer Science
Journal name in source: THEORETICAL COMPUTER SCIENCE
Journal acronym: THEOR COMPUT SCI
Number in series: 39
Volume: 412
Issue: 39
First page : 5276
Last page: 5284
Number of pages: 9
ISSN: 0304-3975
DOI: https://doi.org/10.1016/j.tcs.2011.05.032
Abstract
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.
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