On classification of sequences containing arbitrarily long arithmetic progressions
Küçük Resim Yok
Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
World Scientific Publ Co Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Arithmetic Progressions, Ap-Rank, Van Der Waerden's Theorem, Theorem, Primes
Kaynak
International Journal of Number Theory
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
19
Sayı
8
