{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:09Z","timestamp":1753893849808,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Hegarty conjectured for $n\\neq 2, 3, 5, 7$ that \u00a0$\\mathbb{Z}\/n\\mathbb{Z}$ has\u00a0a permutation which destroys all arithmetic progressions mod $n$. For $n\\ge\u00a0n_0$, Hegarty and Martinsson demonstrated that $\\mathbb{Z}\/n\\mathbb{Z}$ has\u00a0a permutation destroying arithmetic progressions. However $n_0\\approx\u00a01.4\\times 10^{14}$ and thus resolving the conjecture in full remained out of\u00a0reach of any computational techniques. Using\u00a0constructions modeled after those used by Elkies and Swaminathan for the\u00a0case of $\\mathbb{Z}\/p\\mathbb{Z}$ with $p$ being prime, this paper\u00a0establishes\u00a0the conjecture in full. Furthermore, our results are completely independent\u00a0of\u00a0the proof given by Hegarty and Martinsson.<\/jats:p>","DOI":"10.37236\/7192","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:33:45Z","timestamp":1578652425000},"source":"Crossref","is-referenced-by-count":0,"title":["On a Conjecture Regarding Permutations which Destroy Arithmetic Progressions"],"prefix":"10.37236","volume":"25","author":[{"given":"Mehtaab","family":"Sawhney","sequence":"first","affiliation":[]},{"given":"David","family":"Stoner","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,5,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p42\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:34:05Z","timestamp":1579217645000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,8]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7192","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,5,8]]},"article-number":"P2.42"}}