On classification of sequences containing arbitrarily long arithmetic progressions

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dc.authoridSertbas, Doga Can/0000-0002-5884-6856|EYIDOGAN, SADIK/0000-0003-4324-9845
dc.authorwosidSertbas, Doga Can/JSK-6611-2023
dc.authorwosidGöral, Haydar/JVP-2064-2024
dc.authorwosidEyidogan, Sadik/C-3518-2018
dc.contributor.authorCelik, Sermin Cam
dc.contributor.authorEyidogan, Sadik
dc.contributor.authorGoral, Haydar
dc.contributor.authorSertbas, Doga Can
dc.date.accessioned2024-07-18T20:48:48Z
dc.date.available2024-07-18T20:48:48Z
dc.date.issued2023
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractIn 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.en_US
dc.identifier.doi10.1142/S1793042123500926
dc.identifier.endpage1952en_US
dc.identifier.issn1793-0421
dc.identifier.issn1793-7310
dc.identifier.issue8en_US
dc.identifier.scopus2-s2.0-85169456491en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage1917en_US
dc.identifier.urihttps://doi.org/10.1142/S1793042123500926
dc.identifier.urihttps://hdl.handle.net/11411/7932
dc.identifier.volume19en_US
dc.identifier.wosWOS:000985141800001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherWorld Scientific Publ Co Pte Ltden_US
dc.relation.ispartofInternational Journal of Number Theoryen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectArithmetic Progressionsen_US
dc.subjectAp-Ranken_US
dc.subjectVan Der Waerden's Theoremen_US
dc.subjectTheoremen_US
dc.subjectPrimesen_US
dc.titleOn classification of sequences containing arbitrarily long arithmetic progressionsen_US
dc.typeArticleen_US

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