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On a Conjecture Regarding Permutations which Destroy Arithmetic Progressions

2018
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Electronic Journal of Combinatorics
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Hegarty conjectured for $n\neq 2, 3, 5, 7$ that $\mathbb{Z}/n\mathbb{Z}$ has a permutation which destroys all arithmetic progressions mod $n$. For $n\ge n_0$, Hegarty and Martinsson demonstrated that $\mathbb{Z}/n\mathbb{Z}$ has a permutation destroying arithmetic progressions. However $n_0\approx 1.4\times 10^{14}$ and thus resolving the conjecture in full remained out of reach of any computational techniques. Using constructions modeled after those used by Elkies and Swaminathan for the case

doi:10.37236/7192
fatcat:3eim74v3ubbvxm6b25c2kkocbm