A variant of the proof of Van der Waerden's theorem by Furstenberg

Sadık Eyidoğan; Ali Arslan Özkurt

doi:10.31801/cfsuasmas.901214

Research Article

Year 2021, Volume: 70 Issue: 2, 1065 - 1072, 31.12.2021

Sadık Eyidoğan , Ali Arslan Özkurt

https://doi.org/10.31801/cfsuasmas.901214

Abstract

References

Birkhoff, G.D., Dynamical Systems, Math. Soc. Coll. Publ., vol 9, Amer. Math. Soc., Providence RI, 1927. https://doi.org/http://dx.doi.org/10.1090/coll/009
Engelking, R., General Topology, Second Edition, Heldermann Verlag, Berlin, 1989. Furstenberg, H., Poincare recurrence and number theory, Bull. of the A. Math. Soc., 5 (3) (1981), 211–234.
Furstenberg, H., Recurrence in Ergodic Theory and Combinatorial Number, Princeton University Press, Princeton, New Jersey, 1981.
Van der Waerden, B.L., Beweis einer baudetschen vermutung, Nieuw Arch. Wisk., 15 (1927), 212–216.

A variant of the proof of Van der Waerden's theorem by Furstenberg

Year 2021, Volume: 70 Issue: 2, 1065 - 1072, 31.12.2021

Sadık Eyidoğan , Ali Arslan Özkurt

https://doi.org/10.31801/cfsuasmas.901214

Abstract

Let $R$ be a commutative ring with identity. In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of $R$ , we will define a metric on $R$ using them. Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].

Keywords

Van der Waerden Theorem, dynamical system, metric space

References

Birkhoff, G.D., Dynamical Systems, Math. Soc. Coll. Publ., vol 9, Amer. Math. Soc., Providence RI, 1927. https://doi.org/http://dx.doi.org/10.1090/coll/009
Engelking, R., General Topology, Second Edition, Heldermann Verlag, Berlin, 1989. Furstenberg, H., Poincare recurrence and number theory, Bull. of the A. Math. Soc., 5 (3) (1981), 211–234.
Furstenberg, H., Recurrence in Ergodic Theory and Combinatorial Number, Princeton University Press, Princeton, New Jersey, 1981.
Van der Waerden, B.L., Beweis einer baudetschen vermutung, Nieuw Arch. Wisk., 15 (1927), 212–216.

There are 4 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Sadık Eyidoğan 0000-0003-4324-9845 Ali Arslan Özkurt 0000-0001-7631-8435
Publication Date	December 31, 2021
Submission Date	March 22, 2021
Acceptance Date	June 29, 2021
Published in Issue	Year 2021 Volume: 70 Issue: 2

Cite

APA	Eyidoğan, S., & Özkurt, A. A. (2021). A variant of the proof of Van der Waerden’s theorem by Furstenberg. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 1065-1072. https://doi.org/10.31801/cfsuasmas.901214
AMA	Eyidoğan S, Özkurt AA. A variant of the proof of Van der Waerden’s theorem by Furstenberg. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):1065-1072. doi:10.31801/cfsuasmas.901214
Chicago	Eyidoğan, Sadık, and Ali Arslan Özkurt. “A Variant of the Proof of Van Der Waerden’s Theorem by Furstenberg”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 1065-72. https://doi.org/10.31801/cfsuasmas.901214.
EndNote	Eyidoğan S, Özkurt AA (December 1, 2021) A variant of the proof of Van der Waerden’s theorem by Furstenberg. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 1065–1072.
IEEE	S. Eyidoğan and A. A. Özkurt, “A variant of the proof of Van der Waerden’s theorem by Furstenberg”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 1065–1072, 2021, doi: 10.31801/cfsuasmas.901214.
ISNAD	Eyidoğan, Sadık - Özkurt, Ali Arslan. “A Variant of the Proof of Van Der Waerden’s Theorem by Furstenberg”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December 2021), 1065-1072. https://doi.org/10.31801/cfsuasmas.901214.
JAMA	Eyidoğan S, Özkurt AA. A variant of the proof of Van der Waerden’s theorem by Furstenberg. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:1065–1072.
MLA	Eyidoğan, Sadık and Ali Arslan Özkurt. “A Variant of the Proof of Van Der Waerden’s Theorem by Furstenberg”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 1065-72, doi:10.31801/cfsuasmas.901214.
Vancouver	Eyidoğan S, Özkurt AA. A variant of the proof of Van der Waerden’s theorem by Furstenberg. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):1065-72.