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In this paper we study random variables which characterise collections of segments in an equiprobable polynomial scheme related by the H-equivalence. We give an upper bound for the variation distance between the distribution of the random variable ξ k (H) equal to the number of collections of H -equivalent segments and the Poisson distribution. We present sufficient conditions for the convergence of the distribution functions of the number of H -equivalent segments in the triangular array scheme of equiprobable polynomial trials to the normal law, the Poisson law, and the compound Poisson law.

Limit distributions of the number of collections of H -equivalent segments in the triangular array scheme of equiprobable polynomial trials