Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/13623
Title: On classification of sequences containing arbitrarily long arithmetic progressions
Authors: Cam Çelik, Şermin
Eyidoğan, Sadık
Göral, Haydar
Sertbaş, Doğa Can
Keywords: Arithmetic progressions
AP-rank
van der Waerden's theorem
Publisher: World Scientific Publishing
Abstract: 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.
URI: https://doi.org/10.1142/S1793042123500926
https://hdl.handle.net/11147/13623
ISSN: 1793-0421
1793-7310
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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