{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:45Z","timestamp":1753893825565,"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>An often cited statement of Baumert in his book Cyclic difference sets\u00a0asserts that four well known families of cyclic $(4t-1,2t-1,t-1)$ difference sets\u00a0are inequivalent, apart from a small number of exceptions with $t&lt; 8$. We are not aware\u00a0of a proof of this statement in the literature.Three of the families discussed by Baumert have analogous constructions in non-cyclic groups.\u00a0We extend his inequivalence statement to a general inequivalence result, for which we provide a complete\u00a0and self-contained proof. We preface our proof with a survey of the four families of difference\u00a0sets, since there seems to be some confusion in the literature between the cyclic and non-cyclic cases.<\/jats:p>","DOI":"10.37236\/2277","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:58:44Z","timestamp":1578711524000},"source":"Crossref","is-referenced-by-count":0,"title":["Inequivalence of Difference Sets: On a Remark of Baumert"],"prefix":"10.37236","volume":"20","author":[{"given":"Padraig","family":"\u00d3 Cath\u00e1in","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,2,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:26:50Z","timestamp":1579260410000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2277","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,2,25]]},"article-number":"P38"}}