{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T09:47:39Z","timestamp":1770889659975,"version":"3.50.1"},"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>For a finite abelian group $G$ and positive integers $m$ and $h$, we let $$\\rho(G, m, h) = \\min \\{ |hA| \\; : \\; A \\subseteq G, |A|=m\\}$$ and$$\\rho_{\\pm} (G, m, h) = \\min \\{ |h_{\\pm} A| \\; : \\; A \\subseteq G, |A|=m\\},$$ where $hA$ and $h_{\\pm} A$ denote the $h$-fold sumset and the $h$-fold signed sumset of $A$, respectively. The study of $\\rho(G, m, h)$ has a 200-year-old history and is now known for all $G$, $m$, and $h$. Here we prove that $\\rho_{\\pm}(G, m, h)$ equals $\\rho (G, m, h)$ when $G$ is cyclic, and establish an upper bound for $\\rho_{\\pm} (G, m, h)$ that we believe gives the exact value for all $G$, $m$, and $h$.<\/jats:p>","DOI":"10.37236\/4881","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:43:12Z","timestamp":1578699792000},"source":"Crossref","is-referenced-by-count":5,"title":["The Minimum Size of Signed Sumsets"],"prefix":"10.37236","volume":"22","author":[{"given":"B\u00e9la","family":"Bajnok","sequence":"first","affiliation":[]},{"given":"Ryan","family":"Matzke","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,6,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:15:41Z","timestamp":1579256141000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,15]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/4881","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,15]]},"article-number":"P2.50"}}