Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
430920 | Journal of Discrete Algorithms | 2012 | 7 Pages |
Abstract
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 11–14.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Frantisek Franek, Robert C.G. Fuller, Jamie Simpson, W.F. Smyth,