Affordable Access

Publisher Website

More results on overlapping squares

Authors
Journal
Journal of Discrete Algorithms
1570-8667
Publisher
Elsevier
Volume
17
Identifiers
DOI: 10.1016/j.jda.2012.03.003
Keywords
  • Square
  • Period
  • Periodicity
  • Repetition
  • Combinatorics Of Words
Disciplines
  • Mathematics

Abstract

Abstract Three recent papers (Fan et al., 2006; Simpson, 2007; Kopylova and Smyth, 2012) [5,11,8] have considered in complementary ways the combinatorial consequences of assuming that three squares overlap in a string. In this paper we provide a unifying framework for these results: we show that in 12 of 14 subcases that arise the postulated occurrence of three neighboring squares forces a breakdown into highly periodic behavior, thus essentially trivial and easily recognizable. In particular, we provide a proof of Subcase 4 for the first time, and we simplify and refine the previously established results for Subcases 11–14.

There are no comments yet on this publication. Be the first to share your thoughts.