{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:28Z","timestamp":1753893808871,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $(G, +)$ be an abelian group. In 2004, Eliahou and Kervaire found an explicit formula for the smallest possible cardinality of the sumset $A+A$, where $A \\subseteq G$ has fixed cardinality $r$. We consider instead the smallest possible cardinality of the difference set $A-A$, which is always greater than or equal to the smallest possible cardinality of $A+A$ and can be strictly greater. We conjecture a formula for this quantity and prove the conjecture in the case that $G$ is an elementary abelian $p$-group. This resolves a conjecture of Bajnok and Matzke on signed sumsets.<\/jats:p>","DOI":"10.37236\/5502","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:16:30Z","timestamp":1578651390000},"source":"Crossref","is-referenced-by-count":0,"title":["Sets with Few Differences in Abelian Groups"],"prefix":"10.37236","volume":"25","author":[{"given":"Mitchell","family":"Lee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2018,8,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:29:59Z","timestamp":1579217399000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i3p19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,10]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/5502","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,8,10]]},"article-number":"P3.19"}}