More results on overlapping squares ?
Three recent papers (Fan et al., 2006; Simpson, 2007; Kopylova and Smyth, 2012) [5], [11]and[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 1114.
square period period periodicity repetition combinatorics of words