| Autor: |
Çam Çelik, Şermin, Eyidoğan, Sadık, Göral, Haydar, Sertbaş, Doğa Can |
| Předmět: |
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| Zdroj: |
International Journal of Number Theory; Sep2023, Vol. 19 Issue 8, p1917-1952, 36p |
| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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