More results on overlapping squares

Authors:
Frantisek Franek;Robert C. G. Fuller;Jamie Simpson;W. F. Smyth
Affiliations:
Algorithms Research Group, Department of Computing & Software, McMaster University, Hamilton, Ontario L8S 4K1, Canada;Algorithms Research Group, Department of Computing & Software, McMaster University, Hamilton, Ontario L8S 4K1, Canada;Department of Mathematics & Statistics, Curtin University, GPO Box U1987, Perth, WA 6845, Australia;Algorithms Research Group, Department of Computing & Software, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Venue:
Journal of Discrete Algorithms
Year:
2012

Citing 6
Cited 1

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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.