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- W4363672317 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 [Formula: see text] 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." @default.
- W4363672317 created "2023-04-11" @default.
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- W4363672317 date "2023-05-09" @default.
- W4363672317 modified "2023-09-24" @default.
- W4363672317 title "On classification of sequences containing arbitrarily long arithmetic progressions" @default.
- W4363672317 doi "https://doi.org/10.1142/s1793042123500926" @default.
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