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Results tagged with sequences-and-series
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user 168142
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
7
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answer
263
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Analogue to Szemerédi's theorem for non-monotone sequences
Szemerédi's theorem states that a strictly increasing sequence of positive integers $a_0, a_1, \ldots$ whose range has positive density contains arbitrarily long arithmetic progressions (as subsequenc …
- 807
2
votes
Accepted
Analogue to Szemerédi's theorem for non-monotone sequences
It appears the statement is false. The paper "On permutations containing no long arithmetic progressions," by Davis, Entringer, Graham, and Simmons [Acta Arithmetica 34 (1977)] exhibits a permutation …
- 807