{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:27Z","timestamp":1753893867534,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A permutation $\\pi$ of an abelian group $G$ is said to destroy arithmetic progressions (APs) if, whenever $(a, \\, b, \\, c)$ is a non-trivial 3-term AP in $G$, that is $c-b=b-a$ and $a, \\, b, \\, c$ are not all equal, then $(\\pi(a), \\, \\pi(b), \\pi(c))$ is not an AP. In a paper from 2004, the first author conjectured that such a permutation exists of $\\mathbb{Z}_n$, for all $n \\not\\in \\{2, \\, 3, \\, 5, \\, 7\\}$. Here we prove, as a special case of a more general result, that such a permutation exists for all $n \\geq n_0$, for some explicitly constructed number $n_0 \\approx 1.4 \\times 10^{14}$. We also construct such a permutation of $\\mathbb{Z}_p$ for all primes $p &gt; 3$ such that $p \\equiv 3 \\; ({\\hbox{mod $8$}})$.<\/jats:p>","DOI":"10.37236\/5340","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:23:46Z","timestamp":1578695026000},"source":"Crossref","is-referenced-by-count":0,"title":["Permutations Destroying Arithmetic Progressions in Finite Cyclic Groups"],"prefix":"10.37236","volume":"22","author":[{"given":"Peter","family":"Hegarty","sequence":"first","affiliation":[]},{"given":"Anders","family":"Martinsson","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,12,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p39\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:07:40Z","timestamp":1579255660000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/5340","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,12,11]]},"article-number":"P4.39"}}