
Be the first to like this
Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.
Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.
Published on
Thue showed that there exist arbitrarily long squarefree strings over an alphabet of three symbols (not true for two symbols). An open problem was posed, which is a generalization of Thue’s original result: given an alphabet list L = L1, . . . , Ln, where Li = 3, is it always possible to find a squarefree string, w = w1w2 . . . wn, where wi ∈ Li? In this paper we show that squares can be forced on squarefree strings over alphabet lists iff a suffix of the squarefree string conforms to a pattern which we term as an offending suffix. We also prove properties of offending suffixes. However, the problem remains tantalizingly open.
Be the first to like this
Be the first to comment