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It is proved that the number g(q, 5, n) of words of length n over a ^-letter alphabet such that the length of any subword consisting of one and the same letter is no greater than s is very close to λ", where λ is the greatest real root of the polynomial Jt**1 — qx? + q — 1. A representation of λ in the form of a series is found. The results obtained let us calculate asymptotical values of g(q, st n) and the function h(q, s, n) = g(q, s, n) — g(q, s — l, n) as n -» «> for j > c log n, where c is an arbitrary positive constant. The research was supported by the Russian Foundation for Basic Research, grants 96-01-01614, 96- 01-01893, and 96-01-01496, respectively, for each of the authors.

The number of q- ary words with restrictions on the length of the maximal run