{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T12:38:23Z","timestamp":1768999103921,"version":"3.49.0"},"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 $G$, The Erd\u0151s-Ginzburg-Ziv constant $\\mathfrak{s}(G)$ is the smallest $s$ such that every sequence of $s$ (not necessarily distinct) elements of $G$ has a zero-sum subsequence of length $\\operatorname{exp}(G)$. For a prime $p$, let $r(\\mathbb{F}_p^n)$ denote the size of the largest subset of $\\mathbb{F}_p^n$ without a three-term arithmetic progression. Although similar methods have been used to study $\\mathfrak{s}(G)$ and $r(\\mathbb{F}_p^n)$, no direct connection between these quantities has previously been established. We give an upper bound for $\\mathfrak{s}(G)$ in terms of $r(\\mathbb{F}_p^n)$ for the prime divisors $p$ of $\\operatorname{exp}(G)$. For the special case $G=\\mathbb{F}_p^n$, we prove $\\mathfrak{s}(\\mathbb{F}_p^n)\\leq 2p\\cdot r(\\mathbb{F}_p^n)$. Using the upper bounds for $r(\\mathbb{F}_p^n)$ of Ellenberg and Gijswijt, this result improves the previously best known upper bounds for $\\mathfrak{s}(\\mathbb{F}_p^n)$ given by Naslund.\u00a0<\/jats:p>","DOI":"10.37236\/7275","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:34:06Z","timestamp":1578652446000},"source":"Crossref","is-referenced-by-count":9,"title":["Erd&amp;#337;s-Ginzburg-Ziv Constants by Avoiding Three-Term Arithmetic Progressions"],"prefix":"10.37236","volume":"25","author":[{"given":"Jacob","family":"Fox","sequence":"first","affiliation":[]},{"given":"Lisa","family":"Sauermann","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,4,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:34:25Z","timestamp":1579217665000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,27]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7275","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,27]]},"article-number":"P2.14"}}