Limit distributions of the number of absent chains of identical outcomes

We prove the asymptotic normality of the number of absent $s$-chains of identical outcomes in the equiprobable polynomial scheme under the condition that the number of trials $n$ and the number of outcomes $N$ tend to infinity in such a way that $\alpha_N=n/N^s\to\alpha$, $0\le\alpha<\infty$, $N\alpha_N^2\to\infty$.