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

Sadık Eyidoğan; Ali Arslan Özkurt

doi:10.31801/cfsuasmas.901214

Araştırma Makalesi

Yıl 2021, Cilt: 70 Sayı: 2, 1065 - 1072, 31.12.2021

Sadık Eyidoğan , Ali Arslan Özkurt

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

Öz

Kaynakça

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

Yıl 2021, Cilt: 70 Sayı: 2, 1065 - 1072, 31.12.2021

Sadık Eyidoğan , Ali Arslan Özkurt

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

Öz

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].

Anahtar Kelimeler

Van der Waerden Theorem, dynamical system, metric space

Kaynakça

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.

Toplam 4 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Research Article
Yazarlar	Sadık Eyidoğan 0000-0003-4324-9845 Ali Arslan Özkurt 0000-0001-7631-8435
Yayımlanma Tarihi	31 Aralık 2021
Gönderilme Tarihi	22 Mart 2021
Kabul Tarihi	29 Haziran 2021
Yayımlandığı Sayı	Yıl 2021 Cilt: 70 Sayı: 2

Kaynak Göster

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. Aralık 2021;70(2):1065-1072. doi:10.31801/cfsuasmas.901214
Chicago	Eyidoğan, Sadık, ve 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, sy. 2 (Aralık 2021): 1065-72. https://doi.org/10.31801/cfsuasmas.901214.
EndNote	Eyidoğan S, Özkurt AA (01 Aralık 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 ve 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., c. 70, sy. 2, ss. 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 (Aralık 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 ve 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, c. 70, sy. 2, 2021, ss. 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.