О последовательности первых двоичных цифр дробных частей значений многочлена

A. Ya Belov; G. V. Kondakov; I. V. Mitrofanov; M. M. Golafshan; Ivan Andreevich Reshetnikov

doi:10.22405/2226-8383-2021-22-1-482-487

О последовательности первых двоичных цифр дробных частей значений многочлена

Translated title of the contribution: On the sequence of the first binary digits of the fractional parts of the values of a polynomial

A. Ya Belov, G. V. Kondakov, I. V. Mitrofanov, M. M. Golafshan, Ivan Andreevich Reshetnikov

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.22405/2226-8383-2021-22-1-482-487
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

Access to Document

10.22405/2226-8383-2021-22-1-482-487

Cite this

@article{6e1cde3855cd4c2190e4d47fb6a50bed,

title = "О последовательности первых двоичных цифр дробных частей значений многочлена",

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{\textquoteright}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",

author = "Belov, {A. Ya} and Kondakov, {G. V.} and Mitrofanov, {I. V.} and Golafshan, {M. M.} and Reshetnikov, {Ivan Andreevich}",

year = "2021",

doi = "10.22405/2226-8383-2021-22-1-482-487",

language = "רוסית",

volume = "22",

pages = "482--487",

journal = "Chebyshevskii Sbornik",

issn = "2226-8383",

publisher = "State Lev Tolstoy Pedagogical University",

number = "1",

}

TY - JOUR

T1 - О последовательности первых двоичных цифр дробных частей значений многочлена

AU - Belov, A. Ya

AU - Kondakov, G. V.

AU - Mitrofanov, I. V.

AU - Golafshan, M. M.

AU - Reshetnikov, Ivan Andreevich

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Combinatorics on words

KW - Symbolical dynamics

KW - Unipotent torus transformation

KW - Weiyl lemma

UR - http://www.scopus.com/inward/record.url?scp=85105308800&partnerID=8YFLogxK

U2 - 10.22405/2226-8383-2021-22-1-482-487

DO - 10.22405/2226-8383-2021-22-1-482-487

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85105308800

SN - 2226-8383

VL - 22

SP - 482

EP - 487

JO - Chebyshevskii Sbornik

JF - Chebyshevskii Sbornik

IS - 1

ER -

О последовательности первых двоичных цифр дробных частей значений многочлена

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this