The Poisson approximation for the number of matches of values of a discrete function on segments of a sequence of random variables

We find conditions which are sufficient for convergence of the distribution of the number of matches of values of a function considered on tuples of arguments taken from a sequence of independent identically distributed random variables to the Poisson law and estimate the convergence rate. We derive a series of corollaries of this result. In particular, in the equiprobable polynomial scheme we obtain Poisson limit theorems for the number of pairs of non-overlapping tuples with identical frequencies of occurrences of symbols and for the number of pairs of tuples with identical structure.