On the asymptotics of the number of binary words with a given length of a maximal series ?
Let Bs(n) denote the set of binary words of length n whose longest series have the length s. The problem is to find the asymptotic expressions for the size of Bs(n) for any n and s, 1?s?n, as n??. Here the answer is given, whenever as n??. The remaining values of s will be considered in subsequent papers.
asymptotics word series symbol sequence