{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:19Z","timestamp":1753893799529,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A permutation $\\pi$ of an abelian group $G$ (that is, a bijection from $G$ to itself) will be said to avoid arithmetic progressions if there does not exist any triple $(a,b,c)$ of elements of $G$, not all equal, such that $c-b=b-a$ and $\\pi(c)-\\pi(b)=\\pi(b)- \\pi(a)$. The basic question is, which abelian groups possess such a permutation? This and problems of a similar nature will be considered.<\/jats:p>","DOI":"10.37236\/1792","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:21:20Z","timestamp":1578702080000},"source":"Crossref","is-referenced-by-count":5,"title":["Permutations Avoiding Arithmetic Patterns"],"prefix":"10.37236","volume":"11","author":[{"given":"Peter","family":"Hegarty","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,6,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r39\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:02:21Z","timestamp":1579305741000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,6,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1792","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,6,16]]},"article-number":"R39"}}