Some Remarks on Goncharov’s Paper from the Domain of Combinatorics

This note contains some results on the asymptotic distribution of the random vector $(\nu_1,\nu_2,\dots,\nu _{k- 1},\nu_k)$, where $\nu_1,\nu_2,\dots,\nu _{k-1},\nu_k$ are the numbers of $A$-series of lengths $1,2,\dots,k-1$ greater or equal to $k$, respectively, in the simple homogeneous Markov chain with two states $A$ and $B$. The asymptotic distribution of the above-mentioned vector (when appropriately formed) is shown to be multivariate normal with the parameters of the distribution calculated.
Possible extensions for a number of states greater than two are also discussed.