@article {IOPORT.01698517, author = {Korshunov, A.D.}, title = {On the asymptotics of the number of binary words with a given length of a maximal series.}, year = {2001}, journal = {Discrete Applied Mathematics}, volume = {114}, number = {1-3}, issn = {0166-218X}, pages = {171-201}, publisher = {Elsevier Science B.V. (North-Holland), Amsterdam}, doi = {10.1016/S0166-218X(00)00369-3}, abstract = {Summary: Let $B_s(n)$ 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 $B_s(n)$ for any $n$ and $s$, $1\le s\le n$, as $n\to\infty$. Here the answer is given, whenever $s\ge {1\over 2}\log n+2\log\log n$ as $n\to\infty$. The remaining values of $s$ will be considered in subsequent papers.}, identifier = {01698517}, }