FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 1, PAGES 71-79

Inverse problems of symbolic dynamics

A.Ya.Belov
G.V.Kondakov

Let P(n) be a polynomial with irrational greatest coefficient. Let also a superword W $(W = (w_n), n \in \mathbb{N})$ be the sequence of first binary digits of {P(n)}, i.e. wn = [2 {P(n)}], and T(k) be the number of different subwords of W whose length is equal to k. The main result of the paper is the following:

Theorem 1.1. For any n there exists a polynomial Q(k) such that if deg (P) = n, then T(k) = Q(k) for all sufficiently large k.

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