Abstract:
Let $P(n)$ be a polynomial, having an irrational coefficient of the highest degree. A word $w$$(w=(w_n), n\in \mathbb{N})$ consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote by $T(k)$ the number of different subwords of $w$ of length $k$ . We'll formulate the main result of this paper.
Theorem.There exists a polynomial$Q(k)$, depending only on the power of the polynomial$P$, such that$T(k)=Q(k)$for sufficiently great$k$.
Keywords:Combinatorics on words, symbolical dynamics, unipotent torus transformation, Weiyl lemma.