Abstract
Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word w (w = (wn), n ∈ N) consists of a sequence of first binary numbers of {P(n)} i.e. wn = [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.
| Translated title of the contribution | On the sequence of the first binary digits of the fractional parts of the values of a polynomial |
|---|---|
| Original language | Russian |
| Pages (from-to) | 482-487 |
| Number of pages | 6 |
| Journal | Chebyshevskii Sbornik |
| Volume | 22 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2021 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021 State Lev Tolstoy Pedagogical University. All rights reserved.
Keywords
- Combinatorics on words
- Symbolical dynamics
- Unipotent torus transformation
- Weiyl lemma
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