On classification of sequences containing arbitrarily long arithmetic progressions

被引：0

作者：

Celik, Sermin Cam ^{[1
]}

Eyidogan, Sadik ^{[2
]}

Goral, Haydar ^{[3
]}

Sertbas, Doga Can ^{[2
]}

机构：

[1] Istanbul Bilgi Univ, Dept Math, Istanbul, Turkiye

[2] Cukurova Univ, Dept Math, Adana, Turkiye

[3] Izmir Inst Technol, Dept Math, Izmir, Turkiye

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2023年 / 19卷 / 08期

关键词：

Arithmetic progressions; AP-rank; van der Waerden's theorem; THEOREM; PRIMES;

D O I：

10.1142/S1793042123500926

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the classification of sequences containing arbitrarily long arithmetic progressions. First, we deal with the question how the polynomial map n(s) can be extended so that it contains arbitrarily long arithmetic progressions. Under some growth conditions, we construct sequences which contain arbitrarily long arithmetic progressions. Also, we give a uniform and explicit arithmetic progression rank bound for a large class of sequences. Consequently, a dichotomy result is deduced on the finiteness of the arithmetic progression rank of certain sequences. Therefore, in this paper, we see a way to determine the finiteness of the arithmetic progression rank of various sequences satisfying some growth conditions.

引用

页码：1917 / 1952

页数：36

共 21 条

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Andreescu T., 2007, PUTNAM

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