{"paper":{"title":"On A Conjecture Regarding Permutations Which Destroy Arithmetic Progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"David Stoner, Mehtaab Sawhney","submitted_at":"2017-08-01T03:18:49Z","abstract_excerpt":"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 an arithmetic-progression destroying permutation. However $n_0\\approx 1.4\\times 10^{14}$ and thus resolving the conjecture in full remained out of reach of any computational techniques. However, this paper using constructions modeled after those used by Elkies and Swaminathan for the case of $\\mathbb{Z}/p\\mathbb{Z}$ with $p$ being prime, establish the conjecture in ful"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00144","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}