Abstract

The word complexity function p(n) of a sequence x measures the number of n-letter words appearing in sequences in x. A useful heuristic is that sequences with low word complexity have highly constrained dynamical behavior when associated with the shift action. I'll give history of this area and describe a variety of results exhibiting this phenomenon, including recent work with Darren Creutz, where we show that 1.5n is a sharp threshold for a variety of dynamical behaviors.