Extremal functions for sequences (Q1916110)

This paper deals with a certain kind of finite sequences of symbols having no immediate repetition and with no alternating subsequence of length \(s\). Strong upper and lower bounds on the maximum length of such sequences with \(n\) symbols are well known. In this paper the author discusses some properties of the generalization of this concept and goes on to show that the extremal functions of \(aa\dots abb\dots baa\dots abb\dots b\) grow linearly.