A1 Journal article – refereed

On the number of frames in binary words

List of 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 number: 412

Issue number: 39

Number of pages: 9

ISSN: 0304-3975

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.