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\iteman{io-port 05833554}
\itemau{LeSaulnier, Timothy D.; Vijay, Sujith}
\itemti{On permutations avoiding arithmetic progressions.}
\itemso{Discrete Math. 311, No. 2-3, 205-207 (2011).}
\itemab
Summary: We improve the lower bound on the number of permutations of $\{ 1,2,\ldots ,n \}$ in which no 3-term arithmetic progression occurs as a subsequence, and derive lower bounds on the upper and lower densities of subsets of the positive integers that can be permuted to avoid 3-term and 4-term APs. We also show that any permutation of the positive integers must contain a 3-term AP with odd common difference as a subsequence, and construct a permutation of the positive integers that does not contain any 4-term AP with odd common difference.
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\itemcc{}
\itemut{arithmetic progressions; permutations}
\itemli{doi:10.1016/j.disc.2010.10.006}
\end