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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2021 / Volume: 70 Issue: 2

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

Sadık Eyidoğan(Çukurova University)0000-0003-4324-9845
Ali Arslan Özkurt(Çukurova University)0000-0001-7631-8435
Sayfa
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Yayın Tarihi
2021-12-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let R R be a commutative ring with identity.
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Temel Bulgular & Veri:In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of R R , we will define a metric on R R using them.
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Sonuç & Katkı:Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Van der Waerden Theorem · dynamical system · metric space

Abstract

Let R 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 R , we will define a metric on R 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].

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Bu Makaleye Atıf Yap

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, Volume: 70 Issue: 2. https://doi.org/10.31801/cfsuasmas.901214

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Kaynakça (4)

  1. 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
  2. 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.
  3. Furstenberg, H., Recurrence in Ergodic Theory and Combinatorial Number, Princeton University Press, Princeton, New Jersey, 1981.
  4. Van der Waerden, B.L., Beweis einer baudetschen vermutung, Nieuw Arch. Wisk., 15 (1927), 212–216.